CURRICULUM VITAE

 

DORON S. LUBINSKY

 

July 2008

 


LUBINSKY, DORON S…… ……….School of Mathematics

Georgia Institute of Technology,

Atlanta, Georgia 30332-0160

 

EDUCATION:

1978-1980:  Ph.D student at Witwatersrand University. Thesis Title:  “Exceptional Sets of Padé Approximants.”

 

1977: Bachelor of Science Honours in Applied Mathematics, Witwatersrand University.

 

1977: Bachelor of Science Honours in Pure Mathematics, Witwatersrand University.

 

1974-1975: Bachelor of Science majoring in Mathematics, Applied Mathematics and Computer Science, Witwatersrand University.

 

1973: Bachelor of Science (first year), University of South Africa.

 

EMPLOYMENT:

2001 – Present: Professor, School of Mathematics, Georgia Institute of Technology

 

1989 – 2001     Professor, Mathematics Department, Witwatersrand University.

 

1989 - 1989:    Visiting Professor at University of South Florida, Tampa, Florida.

 

1987 - 1989:    Part time Professor, Mathematics Department, Witwatersrand University.

 

1982 - 1988:    Researcher, NRIMS, CSIR, Pretoria.

 

1985 - 1986:    Visiting Professor at University of South Florida, Tampa, Florida. (On study

                         leave from CSIR)

 

1982 - 1982:    Visiting lecturer at Witwatersrand University.

 

1980 - 1982:    Postdoctoral fellow at Technion, I.I.T., Haifa, Israel.

 

 

FELLOWSHIPS & AWARDS:

2008: Freshman Council Burdell's Professor of the Year Award.
2008: Women in Science and Engineering (WISE) Faculty Award.

2000: Millenium Medal from the South African Maths Society for Research

1994: Elected a fellow of the Royal Society of South Africa.

1993: Vice-Chancellor's Research Award for 1994 (jointly with U. Ripamonti).

1989: A-rating for research, awarded by the Foundation for Research and Development.

1986: South African Mathematical Society Award for research in Orthogonal Polynomials.

1980-1982: Lady Davis Postdoctoral Fellowship at Technion, I.I.T., Israel.

1978-1980: AECI Postgraduate Research Fellowship, Witwatersrand University.

1976-1977: CSIR and Senior Bursaries and Lawenski Scholarship, Witwatersrand University.

1976-1977: UNICO Medals for best B.Sc. Hons. student (joint award).

1975: William Cullen Medal for best B.Sc. graduate (joint award); Herbert le May medal for best Applied Maths Major (joint award).

RESEARCH GRANTS
1989-2001: A rating from the National Research Foundation, with grant support.
2004-2006: NSF Individual Grant DMS-0400446
2004: NSF Grant for Constructive Function Theory Tech-04.
2005-2007: BSF Award (Israel-US Binational Science Foundation award) with PI Avram Sidi (Technion) and Eli Levin (Open University of Israel)
2007-2009: NSF Individual Grant DMS-0700427

 

EDITORIAL WORK:

Associate Editor for:
1) Journal of Approximation Theory;
2) Constructive Approximation (1990 - );
3) Quaestiones Mathematicae (Journal of the S. A. Math. Soc.) (1990 - );
4) ETNA (Electronic Transactions on Numerical Analysis) (1995-2003) (2006 - );
5) Computational Methods and Function Theory (2001 - );
6) Chief Guest Editor for the Proceedings of Constructive Functions Tech-04 (appeared as Volume 25 of ETNA).

REFEREEING:

Transactions of the AMS;   Proceedings of the AMS; Israel Journal of Math;  Journal of the London Math. Soc.; Annals of Math;

SIAM Journal of Math. Anal.;  SIAM Journal of Matrix Anal and its Applns.;   SIAM Journal of Numerical Analysis; Mathematics of Computation; Journal of Approximation Theory; J. d"Analyse Math., Journal of Mathematical Physics,

Constructive Approximation; Rocky Mountain Jour. Math.;  Journal of Australian Math. Soc.

Acta Mathematica (Sweden); Acta Mathematica Hungarica; Journal of Comp. and Applied Maths.;  Journal of Math. Anal. and Applns.; Facultatis Nis (ex Yugoslavia); Analysis (International J. Analysis and Applns.); Revista Colombiana de Matematicas; Publicationes Mathematicae Debrecen; Linear Algebra and its Applications; Methods and Applications of Analysis; Studia Mathematica; J. Math. Soc. Japan; International Maths Research Notices (Duke University); Journal of Statistical Physics; Mathematische Annalen.

 

 

TEACHING:

Georgia Institute of Technology:

Fall 2008                       Math8900      Potential Theory                
Spring 2008                   Math1502      Calculus II                        About  490 students at start                     
Fall 2007                       Math1502    Calculus II                          231 students at end

Fall 2007                      Math8900     Special Problems               1 student

Summer 2007                Math8823     Orthogonal Polynomials         2 students
Spring 2007                   Math 1502    Calculus II                           490 students at start, 460 at end
Fall 2006                       Math 6327   Graduate Real Analysis            about 9 students 
Spring 2006                   Math1502     Calculus II                          about 340 students
Fall 2005                       Math6327     Graduate Real Analysis          18 students
Spring 2005                   Math1502     Calculus II                         about 290 students
Fall 2004                       Math4318    Analysis II                             14 students         
Summer  2004              Math8803     Orthogonal Polynomials        1 student

Spring 2004                  Math4317    Real Analysis                      about 40 students
Spring2004                  Math1502   Calculus II                            about 165 students
Fall 2003                      Math 8823   Potential Theory                   5 students

Summer 2003               Math6584     Special Functions                about 20 students

Summer 2003               Math1502      Calculus II                          about 150 students

Spring 2002                  Math1502      Calculus II                          about 180 students

Spring 2003                  Math 4318      Analysis II                          about  30 students                     

Fall 2002                     Math 4317      Real Analysis                          33 students

Summer 2002              Math 1502      Calculus II                             110 students

Spring 2002                 Math 4305       Topics in Linear Algebra           38 students

Spring 2002                  Math 4318       Analysis II                                22 students

Fall 2001                      Math 4317       Real Analysis                            35 students

 

Administration at Georgia Tech
1) Member, secretary, of Graduate Committee
2) Member of Committee to Select VIGRE Postdocs
3) Organiser of  “Constructive Functions – Tech 04”, November 2004.
4) Member of the Organising Committee of IDOMAT 2004, Dortmund, Germany.
5) Member, Acting Chair, of Promotions and Tenure Committee


Conference Organization
1) Chief organizer, Constructive Functions Tech-04, November 7-9, 2004, Georgia Tech, in honor of Ed Saff.

2) Co-organizer, Special session on approximation theory, conference in honor of Charles Chui, Athens GA, May 2005.

3) Special Session on approximation theory, AMS Sectional meeting, Miami, April 2, 2006.
4) Workshop on polynomials, Banff, November 2007.


Ph.D. STUDENTS:

1) A. Knopfmacher (1983-1985)

2) L. Pretorius (1987 co-promoter)

3) K. Driver (1988-1991)

4) T. Mthembu (1988-1991)

5) D.M. Matjila (1991-1994)

6) S.B. Damelin (1993 -1995)

7) P. Zhou (1995-1996)

8) D. Kubayi (1998 - 2001)

9) H.P. Mashele (1998 - 2001)

10) C.K. Kobindarajah (2000-2001)
11) Ulfar Stefansson (2006- )

 

M.Sc. STUDENTS:

1) I. Momoniat (1983-1985)

2) G. Coppin (1988-1990)

3) K. Engelbrecht (1990-1991)

4) P. Brown (1992-1993)

5) S.B. Damelin (1992-1993)

6) P. Zhou (1993-1994)

7) L. Gcilitshana (1995-1998)

8) J.B. Gyamfi-Owusu (1995-1997)

9) D. Kubayi (1996-1998)

10) C.K. Kobindarajah (1998)

11) D.S. Rusznyak (co-supervisor) (1998)

12) K. Morris (co-supervisor) (2001)

REU Students
Ioanna Soran (June/July 2005)
Beth Hart (May/June/July 2006)

Jeremy McKibben-Sanders (June/July 2008)


RESEARCH INTERESTS:

1) Orthogonal Polynomials (especially their quantitative behaviour for

exponential weights) with applications to approximation theory, numerical

analysis, harmonic analysis, random matrices;
2) Rational approximation (especially Pad'e approximation);

3) Inequalities, especially involving potential theory and/ or complex analysis;

4) Numerical Integration;
5) q series (especially in the singular case that q is on the unit

circle) and also their applications in irrationality and transcendence theory.

 

BOOKS/LECTURE  NOTES PUBLISHED:
1) Strong Asymptotics for Extremal Polynomials Associated with Weights on (-?? ,?? ) (D.S. Lubinsky and E.B. Saff), Springer Lecture Notes, Vol. 1305, Springer, Berlin, 1988.

 

2) Strong Asymptotics for Extremal Errors Associated with Erdös s-type Weights, Pitman Research Notes, Vol. 202, Longmans, Burnt Mill, Essex, 1989.

 

3) Orthogonal Polynomials for Exponential Weights (A.L. Levin and D.S. Lubinsky), Canadian Mathematical Monographs Series, Vol. 4, Springer, New York, 2001.

 

 

MEMOIRS PUBLISHED:

1) Christoffel Functions and Orthogonal Polynomials for Exponential Weights on [-1,1] (A.L. Levin and D.S. Lubinsky), Memoirs of the Amer. Math. Soc., Vol. 111, No. 535 (146 pages), September 1994.

 

REFEREED PUBLICATIONS:

 

Papers Already Published:

1) Diagonal Pad'e Approximants and Capacity, Journal of Mathematical Analysis and Applications, 78 (1980), 58-67.

 

2) On Non-Diagonal Pad'e Approximants, Journal of Mathematical Analysis and Applications, 78 (1980), 405-428.

 

3) Best Approximation over the Whole Complex Plane (D.S. Lubinsky and O. Shisha), Journal of Approximation Theory, 36 (1982), 277-293.

 

4) Divergence of Complex Rational Approximations, Pacific Journal of Mathematics, 108 (1983), 141-153.

 

5) Geometric Convergence of Lagrangian Interpolation and Numerical Integration Rules, Journal of Approximation Theory, 39 (1983), 338-360.

 

6) On the Largest Zeros of Orthogonal Polynomials for Certain Weights (D.S. Lubinsky and A. Sharif), Mathematics of Computation, 41 (1983), 199-202.

 

7) Convergence of Linear and Nonlinear Pad'e Approximants from Series of Orthogonal Polynomials (D.S. Lubinsky and A. Sidi), Transactions of the American Mathematical Society, 278 (1983), 333-345.

 

8) On the Zeros of Some Polynomials that arise in Numerical Quadrature and Convergence Acceleration (A. Sidi and D.S. Lubinsky), SIAM Journal of Numerical Analysis, 20 (1983), 400-405.

 

9) Convergence of Exponential Interpolation for Completely Bounded Functions (A. Sidi and D.S. Lubinsky), Journal of Approximation Theory, 39 (1983), 185-201.

 

10) On Convergence of Rational and Best Rational Approximations, Journal of Mathematical Analysis and Applications, 98 (1984), 419-434.

 

11) A Weighted Polynomial Inequality, Proceedings of the American Mathematical Society, 92 (1984), 263-267.

 

12) Rates of Convergence of Gaussian Quadrature for Singular Integrands (D.S. Lubinsky and P. Rabinowitz), Mathematics of Computation, 43 (1984), 219-242.

 

13) Product Integration of Logarithmic Singular Integrands Based on Cubic Splines (A. Alaylioglu, D. Eyre and D.S. Lubinsky), Journal of Computational and Applied Mathematics, 11 (1984), 353-366.

 

14) Note on Polynomial Approximation of Monomials and Diophantine Approximation, Journal of Approximation Theory, 43 (1985), 29-35.

 

15) On Nevai's Bounds for Orthogonal Polynomials Associated with Exponential Weights, Journal of Approximation Theory, 44 (1985), 86-91.

 

16) Padé Tables of a Class of Entire Functions, Proceedings of the American Mathematical Society, 94 (1985), 399-405.

 

17) Simultaneous Rational Approximation of a Function and its Derivatives (A.L. Levin and D.S. Lubinsky), Journal of Approximation Theory, 44 (1985), 205-220.

 

18) Padé Tables of Entire Functions of Very Slow and Smooth Growth, Constructive Approximation, 1 (1985), 349-358.

 

19) Estimates of Freud-Christoffel Functions for Some Weights with the Whole Real Line as Support, Journal of Approximation Theory, 44 (1985), 343-379.

 

20) Gaussian Quadrature, Weights on the Whole Real Line and Even Entire Functions with Non-negative Even Order Derivatives, Journal of Approximation Theory, 46 (1986), 297-313.

 

21) Convergence of Product Integration Rules for Functions with Interior and Endpoint Singularities over Bounded and Unbounded Intervals (D.S. Lubinsky and A. Sidi), Mathematics of Computation, 46 (1986), 229-246.

 

22) Best Rational Approximation of Entire Functions whose Maclaurin Series Decrease Rapidly and Smoothly, (A.L. Levin and D.S. Lubinsky), Transactions of the American Mathematical Society, 293 (1986), 533-546.

 

23) Even Entire Functions Absolutely Monotone in (0, ∞) and Weights on the Whole Real Line, in “Orthogonal Polynomials and Their Applications” (C. Brezinski et al, eds.), Springer Lecture Notes in Mathematics, Vol. 1171 (1986), 221-229.

 

24) Freud's Conjecture for Exponential Weights (D.S. Lubinsky, H.N. Mhaskar, E.B. Saff), Bulletin of the Amer. Math. Soc., 15 (1986), 217-221.

 

25) Canonical Products and the Weights exp (- | x  |α ), α >1, with Applications (A.L. Levin and D.S. Lubinsky), Journal of Approximation Theory, 49 (1987), 149-169.

 

26) Weights on the Real Line that admit Good Relative Polynomial Approximation, with Applications (A.L. Levin and D.S. Lubinsky), Journal of Approximation Theory, 49 (1987), 170-195.

 

27) Mean Convergence of Lagrange Interpolation for Freud's Weights with Application to Product Integration Rules (A. Knopfmacher and D.S. Lubinsky), Journal of Computational and Applied Mathematics, 17 (1987), 79-105.

 

28) Asymptotics of Toeplitz Determinants and Rows of the Padé Table, in “Approximation Theory 5,” pp.443-446, Academic Press, New York, 1986.

 

29) Derivatives of Orthogonal Polynomials and Characterization of Weights (S. Bonan, D.S. Lubinsky and P. Nevai), in “Approximation Theory 5,” pp.271-274, Academic Press, New York, 1986.

 

30) Padé Approximation of Partial Theta Functions and the Rogers-Szego Polynomials (D.S. Lubinsky and E.B. Saff), in “Approximation Theory 5,” pp.447-450, Academic Press, New York, 1986.

 

31) Quadrature Sums involving pth Powers of Polynomials (D.S. Lubinsky, A. Máté and P. Nevai), SIAM J. of Math. Anal., 18 (1987), 531-544.

 

32) A Product Quadrature Algorithm for Oscillatory Integrals by Hermite Interpolation (A. Alaylioglu and D.S. Lubinsky), Journal of Computational and Applied Mathematics, 17 (1987), 137-169.

 

33) Convergence theorems for Rows of Differential and Algebraic Hermite-Padé Approximants (George A. Baker, Jr. and D.S. Lubinsky), Journal of Computational and Applied Mathematics, 18 (1987), 29-52.

 

34) Uniform Convergence of Rows of the Padé Table for Functions with Smooth Maclaurin Series Coefficients, Constructive Approximation, 3 (1987), 307-330.

 

35) Orthogonal Polynomials and their Derivatives, II (D.S. Lubinsky, S. Bonan and P. Nevai), SIAM J. Math. Anal., 18 (1987), 1163-1176.

 

36) Polynomial Approximation with Exponential Weights (Z. Ditzian, D.S. Lubinsky, P. Nevai and V. Totik), Acta Math. Hung., 50 (1987), 165-175.

 

37) Convergence of Padé Approximants for the Partial Theta Functions and the Rogers-Szegö Polynomials (D.S. Lubinsky and E.B. Saff), Constructive Approximation, 3(1987), 331-361.

 

38) Analogues of Freud's Conjecture for Erdös Type Weights and Related Polynomial Approximation Problems (A. Knopfmacher and D.S. Lubinsky), in Approximation Theory, Tampa (E.B. Saff, ed.), Springer Lecture Notes in Mathematics, Vol. 1287, pp.21-69, Springer, Berlin, 1987.

 

39) Strong Asymptotics for Lp Extremal Polynomials (1< p < ∞) Associated with Weights on [-1,1]$, (D.S. Lubinsky and E.B. Saff), n Approximation Theory, Tampa (E.B. Saff, ed.), Springer Lecture Notes in Mathematics, Vol. 1287, pp. 83-104, Springer, Berlin, 1987.

 

40) A Survey of General Orthogonal Polynomials for Weights on Finite and Infinite Intervals, Acta Applicandae Mathematicae, 10 (1987), 237-296.

 

41) Markov-Bernstein Inequalities Revisited (D.S. Lubinsky and P. Nevai), (Chinese) Journal of Approximation Theory and its Applications, 3 (1987), 98-119.

 

42) A Proof of Freud's Conjecture for Exponential Weights (D.S. Lubinsky, H.N. Mhaskar and E.B. Saff), Constructive Approximation, 4 (1988), 65-83.

 

43) Uniform and Mean Polynomial Approximation by Certain Weighted Polynomials, with Applications (D.S. Lubinsky and E.B. Saff), Constructive Approximation, 4 (1988), 21-64.

 

44) Freud's Conjecture and Approximation of Reciprocals of Weights by Polynomials (A. Knopfmacher, D.S. Lubinsky and P. Nevai), Constructive Approximation, 4 (1988), 9-20.

 

45) Asymptotic Behaviour of the Ratio of Christoffel Functions for Weights W2 and W2g (A. Knopfmacher and D.S. Lubinsky), Journal of Approximation Theory, 53 (1988), 293-314.

 

46) Padé Tables of Entire Functions of Very Slow and Smooth Growth II, Constructive Approximation, 4 (1988), 321-339.

 

47) Power Series Equivalent to Rational Functions: A Shifting--Origin Kronecker Type Theorem and Normality of Padé Tables, Numerische Mathematik, 54 (1988), 33-40.

 

48) Jump Distributions on [-1,1] Whose Orthogonal Polynomials have Leading Coefficients with Given Asymptotic Behaviour, Proc. AMS, 104 (1988), 516-524.

 

49) Convergence of Interpolation to Transforms of Totally Positive Kernels, (N. Dyn and D.S. Lubinsky), Canadian Journal of Mathematics, 40 (1988), 750-768.

 

50) On Uniform Convergence of Rational, Newton-Pad'e, Interpolants of Type (n,n) with Free Poles as n  → ∞, Numerische Mathematik, 55 (1989), 247-264.

 

51) Non-Interpolatory Integration Rules for Cauchy Principal Value Integrals, (P. Rabinowitz and D.S. Lubinsky), Mathematics of Computation, 53 (1989), 279-295.

 

52) Can We Avoid Non-Normality and Spurious Poles In Padé and Rational Interpolation, in Approximation Theory VI, (eds. C.K. Chui, L.L. Schumaker, J.D. Ward), Academic Press, New York, 1989, pp.405-408.

 

53) Szegö Asymptotics for Non-Szegö Weights on [-1,1] (D.S. Lubinsky and E.B. Saff), in Approximation Theory VI, (eds. C.K. Chui, L.L. Schumaker, J.D. Ward), Academic Press, New York, 1989, pp.409-412.

 

54) Sufficient Conditions for Asymptotics Associated with Weighted Extremal Problems on R, (D.S. Lubinsky and E.B. Saff), Rocky Mountain Journal of Mathematics, 19 (1989), 261-269.

 

55) The Approximate Approach to Orthogonal Polynomials for Weights on  (- ∞, ∞), in Orthogonal Polynomials: Theory and Practice (ed. P. Nevai), NATO ASI Series C Vol. 294, pp.293-310, Kluwer, Dordrecht, 1990.

 

56) L∞  Markov and Bernstein Inequalities for Freud Weights, (A.L. Levin and D.S. Lubinsky), SIAM Journal of Math. Anal., 21(1990), 1066-1082.

 

57) L∞ Markov and Bernstein Inequalities for Erdös Weights, Journal of Approximation Theory, 60(1990), 188-230.

 

58) Coefficient Bounds in the Lorentz Representation of a Polynomial (D.S. Lubinsky and Z. Ziegler), Canadian Math. Bull., 33(1990), 197-206.

 

59) Rows and Diagonals of the Walsh Array for Entire Functions with Smooth Maclaurin Series Coefficients, (A.L. Levin and D.S. Lubinsky), Constructive Approximation, 6(1990), 257-286.

 

60) The Supremum Norm of Christoffel Functions for Erdös Weights, (D.S. Lubinsky and T.Z. Mthembu), Journal of Approximation Theory, 63(1990), 255-266.

 

61) Non-normality of Continued Fraction Partial Quotients Modulo Q, (A. Knopfmacher and D.S. Lubinsky), Revista Colombiana de Matematicas, 24(1990), 179-182.

 

62) Convergence of Pad'e Approximants for Wynn's Power Series II, (K. Driver and D.S. Lubinsky), in Colloquia Mathematica Societatis Janos Bolyai, (Proceedings of Kecskemet Approximation Theory Conference, Hungary) 58(1990): 221-239.

 

63) Singularly Continuous Measures in Nevai's Class M, Proc. Amer. Math. Soc., 111(1991), 413-420.

 

64) Lp Markov-Bernstein Inequalities for Erdös Weights (D.S.Lubinsky and T.Z.Mthembu), Journal of Approximation Theory, 65(1991), 322-340.

 

65) Rational versus Polynomial Approximation of Entire Functions (Proceedings of Erice Conference), IMACS Annals on Computing and Applied Mathematics, 9(1991), 81-86.

 

66) Markov-Bernstein Inequalities for Erdös Weights, (D.S. Lubinsky and T.Z. Mthembu), (Proceedings of Erice Conference), IMACS Annals on Computing and Applied Mathematics, 9(1991), 337-340.

 

67) On the Density of Generalized Polynomials, (N. Dyn, D.S.Lubinsky, and B. Shekhtman), Canadian Math. Bull., 34(1991), 202-207.

 

68) Distribution of Poles of Diagonal Rational Approximants to Functions of Fast Rational Approximability, Constructive Approximation, 7(1991), 501-519.

 

69) Convergence of Padé Approximants for Wynn's Power Series I, (K.Driver and D.S. Lubinsky), Aequationes Mathematicae, 42(1991), 85-106.

 

70) Irregular Distribution of {n β}, n = 1,2,3,...,Quadrature of Singular Integrands, and Curious Basic Hypergeometric Series, (K. Driver, D.S. Lubinsky, G. Petruska and P. Sarnak), Indagationes Mathematicae, 2(1991), 469-481.

 

71) Spurious Poles in Diagonal Rational Approximation, n Progress in Approximation Theory (eds. A.A. Goncar and E.B. Saff), Springer-Verlag, Berlin, 1992, pp. 191-213.

 

72) Orthogonal Expansions and the Error of Weighted Polynomial Approximation for Erdös Weights, (D.S. Lubinsky and T.Z. Mthembu), Numerical Functional Analysis and Optimization, 13(1992), 327-348.

 

73) Hermite and Hermite-Fejer Interpolation Associated with Weights on  R: The L∞ -Theory, (D.S. Lubinsky), Journal of Approximation Theory, 70(1992), 284-334.

 

74) Christoffel Functions, Orthogonal Polynomials, and Nevai’s Conjecture for Freud Weights, (A.L. Levin and D.S. Lubinsky), Constructive Approximation, 8 (1992), 463-535.

 

75) Sub-Exponential Growth of Solutions of Difference Equations, (D.S. Lubinsky and P. Nevai), J. Lond. Math. Soc., 46 (1992), 149-160.

 

76) Hermite and Hermite-Fejer Interpolation Associated with Weights on  R: The L1 Theory, (D.S. Lubinsky and P. Rabinowitz), Canadian J. Math., 44(1992), 561-590.

 

77) Convergence of Simultaneous Hermite-Pad'e Approximants to the n-Tuple of q-Hypergeometric Series {1 ø 1 ((1,1),(c,_γj); z)}nj=1, (M. de Bruin, K.A. Driver and D.S. Lubinsky), Numerical Algorithms, 3 (1992), 185-192.

 

78) Interpolatory Integration Rules and Orthogonal Polynomials with Varying Weights, (T. Bloom, D.S. Lubinsky and H.B. Stahl), Numerical Algorithms, 3 (1992), 55-66.

 

79) Hermite-Fejer Interpolation for Weights on the Whole Real Line, (D.S. Lubinsky and P. Rabinowitz), n Constructive Theory of Functions 91 (eds. K.G. Ivanov, P.P. Petrushev, B.H. Sendov), Publishing House of the Bulgarian Academy of Sciences, Sofia 1992, pp.183-192.

 

80) Irregular Distribution of {n β}; n = 1,2,3,... , and Curious Basic Hypergeometric Series, (K.A. Driver, D.S. Lubinsky, G. Petruska), in Constructive Theory of Functions 91 (eds. K.G. Ivanov, P.P. Petrushev, B.H. Sendov), Publishing House of the Bulgarian Academy of Sciences, Sofia 1992, pp.115-122.

 

81) What Distributions of Points are Possible for Convergent Sequences of Interpolatory Integration Rules? (T. Bloom, D.S. Lubinsky and H. Stahl), Constructive Approximation, 9 (1993), 41-58.

 

82) Distribution of Points for Convergent Interpolatory Integration Rules on (-∞,∞), (T. Bloom, D.S. Lubinsky and H. Stahl), Constructive Approximation, 9 (1993), 59-82.

 

83) Convergence of Padé Approximants for a q-hypergeometric Series (Wynn's Power Series III), (K. Driver and D.S. Lubinsky), Aequationes Mathematicae, 45 (1993), 1-23.

 

84) Markov-Bernstein and Nikolskii Inequalities, and Christoffel Functions for Exponential Weights on [-1,1], (D.S. Lubinsky and E.B. Saff), SIAM J. Math. Anal., 24 (1993), 528-556.

 

85) The Zero Distribution of the Partial Products of Power Product Expansions, (H. Gingold, A. Knopfmacher and D.S. Lubinsky), Analysis, 13 (1993), 133-157.

 

86) On the Degree of Non-Uniqueness of Simultaneous Hermite- Padé Approximants to A Vector of Entire Functions (K.A. Driver and D.S. Lubinsky), Indagationes Mathematicae, 4 (1993), 297-310.

 

87) Pointwise Convergence of Fourier Transforms (D.S. Lubinsky and F. Moricz), Archiv der Mathematik, 61 (1993), 82-87.

 

88) Convergence of Product Integration Rules for Weights on the Whole Real Line, n Contributions in Numerical Mathematics (R.P. Agarwal, Ed.), World Scientific Series in Applicable Analysis, Volume 2, World Scientific, Singapore, 1993, pp.255-270.

 

89) Distributions of Points in Convergent Sequence of Interpolatory Integration Rules: The Rates (D. Lubinsky, T. Bloom, H. Stahl), in Proceedings of Oberwolfach Conference, (H. Brass and G. Hammerlin, eds.), ISNM Series in Numerical Mathematics, Vol. 112, Birkhauser, Basel, 1993,

pp.25-37.

 

90) Convergence of Simultaneous Hermite-Pad'e Approximants to the n -Tuple of q -Hypergeometric Series {2 ø0((A, αj),(1,1); z)}nj=1, (M. de Bruin, K.A. Driver and D.S. Lubinsky), Journal Comp. Applied Maths, 49 (1993), 37-44.

 

91) Bounds for Orthogonal Polynomials for Exponential Weights on (-1,1) and (-∞, ∞), (A.L. Levin and D.S. Lubinsky), Rendiconti del Circolo Matematico di Palermo, 33 (1993), 75-96.

 

92) Behaviour of Alternation Points in Best Rational Approximation, (D. Braess, D. Lubinsky, E.B. Saff), Acta Appl. Math., 33 (1993), 195-210.(Also in Nonlinear Numerical Methods and Rational Approximation II, (ed. A. Cuyt), Kluwer, 1994, pp.159-172).

 

93) An Update on Orthogonal Polynomials and Weighted Approximation on the Real Line, Acta Appl. Mathematicae, 33 (1993), 121-164.

 

94) Mean Convergence of Lagrange Interpolation for Erdös Weights, (D.S. Lubinsky and T.Z. Mthembu), J. Comp. Appl. Math., 47 (1993), 369-390.

 

95) How to Discretise a Logarithmic Potential, (D. Lubinsky and V. Totik), Acta Sci. Math. Szeged., 57(1993), 419-428.

 

96) The Weighted Lp-Norms of Orthonormal Polynomials for Freud Weights, (D.S. Lubinsky and F. Moricz), J. Approx. Theory, 77 (1994),

42-50.

 

97) Best Weighted Polynomial Approximation via Jacobi Expansions (D. Lubinsky and V. Totik), SIAM J. Math. Anal., 25 (1994), 555-570.

 

98) Degree of Approximation by Rational Functions with Prescribed Numerator Degree, (D. Leviatan and D. Lubinsky), Can. J. Math., 46 (1994), 619-633.

 

99) Lp Markov-Bernstein Inequalities for Freud Weights, (A.L. Levin and D.S. Lubinsky), J. Approx. Theory, 77 (1994), 229-248.

 

100) Hermite-Padé Polynomials and Approximation Properties, (K. Driver, D. Lubinsky and H. Wallin), in Nonlinear Numerical Methods and Rational Approximation II (ed. A. Cuyt), Kluwer, 1994, pp.261-268.

 

101) Zeros of Orthogonal and Biorthogonal Polynomials: Some Old, Some New, in Nonlinear Numerical Methods and Rational Approximation II, (ed. A. Cuyt), Kluwer, 1994, pp.3-16.

 

102) Weighted Polynomial Approximation with Freud Weights, (D.S. Lubinsky and V. Totik), Constructive Approximation, 10 (1994), 301-315.

 

103) Rational vs. Polynomial Approximation of Entire Functions, in Linear and Complex Analysis Problem Book 3, (eds. V.P. Havin and N.K. Nikolskii), Springer Lecture Notes, Vol. 1574, Springer, Berlin, 1994, pp. 194-195.

 

104) Christoffel Functions and Orthogonal Polynomials for Erdös Weights, (A.L. Levin, D.S. Lubinsky and T.Z. Mthembu), Rendiconti di Matematica di Roma, 14(1994), 199-289.

 

105) Strong Asymptotics for Polynomials Biorthogonal to Powers of log x, (D.S. Lubinsky and A. Sidi), Analysis, 14(1994), 341-379.

 

106) Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Freud Weights, (D. Lubinsky and D. Matjila), SIAM J. Math. Anal., 26(1995), 238-262.

 

107) Functions of the Second kind for Freud Weights and Series Expansions of Hilbert Transforms, (G. Criscuolo, B.M. Della-Vecchia, D. Lubinsky and G. Mastroianni), J. Math. Anal. Applns., 189(1995), 256-296.

 

108) Orthogonal Polynomials and Christoffel Functions for exp (- |x|α ), α < 1, (A.L. Levin and D.S. Lubinsky), J. Approx. Theory, 80(1995), 219-252.

 

109) Weierstrass’ Theorem in the Twentieth Century: A Selection, Quaestiones Math., 18(1995), 91-130.

 

110) Convergence of Diagonal Padé Approximants for Functions Analytic near 0, Trans. Amer. Math. Soc., 723(1995), 3149-3157.

 

111) An Extension of the Erd"os-Turan Inequality for Sums of Successive Fundamental Polynomials, Annals of Numerical Mathematics (Baltzer AG), 2(1995), 305-309.

 

112) A Survey of Mean Convergence of Orthogonal Polynomial Expansions, Proc. of 2nd Confer. on Function Spaces (Edwardsville, Illinois) (ed. K. Jarosz), Dekker, New York, 1995, pp. 281-310.

 

113) Converse Quadrature Sum Inequalities for Polynomials with Freud Weights, Acta. Scient. Math. (Szeged), 60(1995), 527-557.

 

114) Necessary and Sufficient Conditions for Mean Convergence of Orthogonal Expansions for Freud Weights, (S-W. Jha and D.S. Lubinsky), Constr. Approx., 11(1995), 331-363.

 

115) Full Quadrature Sums for pth Powers of Polynomials with Freud  Weights, (D.S. Lubinsky and D. Matjila), J. Comp. Appl. Math., 60(1995), 285-296.

 

116) Ideas of Weighted Polynomial Approximation on (-∞, ∞), n Proceedings of Aproximation Theory VIII, (eds. C.K. Chui, L.L. Schumaker), World Scientific, Singapore, 1995, pp. 371-396.

 

117) On the Diagonal Padé Approximants of Meromorphic Functions, Indagationes Mathematicae, 7(1996), 97-110.

 

118) Nuttall-Pommerenke Theorems for Homogeneous Approximants, (A. Cuyt, K. Driver, D.S. Lubinsky), J. Comp. Appl. Math., 67(1996), 141-146.

 

119) On The Size of Lemniscates of Polynomials in One and Several Variables, (A. Cuyt, K. Driver, D.S. Lubinsky), Proc. Amer. Math. Soc., 124(1996), 2123-2136.

 

120) Kronecker Type Theorems, Normality and Continuity of the Multivariate Padé Operator (A. Cuyt, K. Driver, D.S. Lubinsky), Numerische Mathematik, 73(1996), 311-328.

 

121) A Direct Approach to Convergence of Multivariate, Non-homogeneous Padé  Approximants, (A. Cuyt, K. Driver, D.S. Lubinsky), J. Comp. Appl. Math., 69(1996), 353-366.

 

122) Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Erdös Weights, (S.B. Damelin and D.S. Lubinsky), Can. Math. J., 40(1996), 710-736.

 

123) Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Erd"os Weights II, (S.B. Damelin and D.S. Lubinsky), Can. Math. J., 40(1996), 737-757.

 

124) Continuing the Fraction, SA Journal of Science, 92(1996), 363-364.

 

125) Jackson and Bernstein Theorems for Exponential Weights, n Approximation Theory and Fourier Series, (eds. P. Vertesi et al.), Janos Bolyai Society, Vol.5, Budapest, 1996, pp. 85-115.

 

126) On the Convergence of Multivariate Pad'e Approximants (A. Cuyt and D.S.Lubinsky), Bulletin de la Societe Mathematique de Belgique, (Special Issue on Numerical Analysis), December 1996, pp. 51-61.

 

127) The Weighted Lp Norms of Orthonormal Polynomials for Erdös Weights, Int. J. for Computers and Mathematics and its Applications, 33(1997), 151-163.

 

128) Jackson and Smoothness Theorems for Freud Weights in Lp (0 < p < ∞ ), (Z. Ditzian and D.S. Lubinsky), Constr. Approx., 13(1997), 99-152.

 

129) A de Montessus Theorem for Multivariate Homogeneous Padé Approximants, (A. Cuyt and D.S. Lubinsky), Annals of Numerical Mathematics, 4(1997), 217-228.

 

130)  Forward and Converse Theorems of Polynomial Approximation for Exponential Weights on [-1,1] I, J. Approx. Theory, 91(1997), 1-47.

 

131) Forward and Converse Theorems of Polynomial Approximation for Exponential Weights on [-1,1] II, J. Approx. Theory, 91(1997), 48-83.

 

133) Small Values of Polynomials: Cartan, Polya and Others, J. Ineq. And Applns., 1(1997), 199-222.

 

133) On the Irrationality of Π∞j = 1 (1 ± q-j r + q-2js) , (P.Zhou and D.S. Lubinsky), Analysis, 17(1997), 129-153.

 

134) On q-Exponential Functions for  | q | =1, Canadian. Math. J., 41(1998), 86-97.

 

135) Smooth Maclaurin Series Coefficients in Padé and Rational Approximation, n Approximation Theory in Memory of A.K. Varma (eds., Z. Nashed, A. Sharma, J. Szabados), Marcel Dekker, New York, 1998, pp. 363-388.

 

136) Jackson Theorems for Erdös Weights in Lp (0 < p < ∞ ), (S.B. Damelin and D.S. Lubinsky) J. Approx. Theory, 94(1998), 333-382.

 

137) Marcinkiewicz-Zygmund Inequalities: Methods and Results, in Recent Progress in Inequalities (ed. G.V. Milovanovic et al.), Kluwer Academic Publishers, Dordrecht, 1998, pp. 213-240.

 

138) Mean Convergence of Lagrange Interpolation for Exponential Weights on [-1,1], Canadian Math. J., 50(1998), 1273-1297.

 

139) Bounds for Orthogonal Polynomials for Exponential Weights (AL Levin and DS Lubinsky), J. Comp. Appl. Math., 99(1998), 475-490.

 

140) Asymptotic Approximation by Entire Functions with Positive Coefficients, in “Approximation Theory and its Applications,” (ed. T. M. Rassias), Hadronic Press, Florida, 1998, pp. 137-158.

 

141) Small Values of Polynomials and Potentials with Lp Normalization, Proc. Amer. Math. Soc., 127(1999), 529-536.

 

142) On Boundedness of Lagrange Interpolation in Lp, p < 1, Journal of Approximation Theory, 96(1999), 399-404.

 

143) Mean Convergence of Extended Lagrange Interpolation with Freud Weights (D.S. Lubinsky and G. Mastroianni), Acta Math. Hungar., 84(1999), 47-63.

 

144) Will Ramanujan kill Baker-Gammel-Wills? (A Selective Survey of Padé Approximation), n Proceedings of IDOMAT 98, International Series in Numerical Mathematics, Vol. 132, Birkhauser, Basel, 1999, pp. 159-174.

 

145) The Size of (q;q)n for q on the Unit Circle, Journal of Number Theory, 76(1999), 217-247.

 

146) Asymptotics Associated with Exponential Weights, (A.L. Levin and D.S. Lubinsky), International Maths Research Notices, 12(1999), 673-683.

 

147) On Converse Marcinkiewicz-Zygmund Inequalities in Lp, p > 1, Constr. Approx., 15(1999), 577-610.

 

148) Convergence of Product Integration Rules for Weights on the Whole Real Line II, in Hammerlin Memorial Volume (ed. R.P. Agarwal), World Scientific, Singapore, 1999, pp. 201-215.

 

149) Weighted Lebesgue Constants (DS Lubinsky and J Szabados), Constr. Approx. (Problem Section), 16(2000), 157-159.