Jeff Geronimo, Professor of Mathematics
School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332
geronimo@math.gatech.edu
Mathematical Interests:
Applied Mathematics: scattering theory, orthogonal
polynomials, dynamical systems, iterated maps, numerical
analysis,wavelets
Current research:
Construction of Spline and Fractal multiwavelets. Spectral properties of
Jacobi matrices. Theory of orthogonal polynomials on the unit circle.
Recent publications:
- Necessary and Sufficient Condition for the limit of Stieljes
Transforms to be a Stieljes Transform" (with T.P. Hill) Accepted Journ. Approx Theory.
- Certain Two Dimensional Integrals that Appear in Conformal Field Theory"
(with H. Navelet) Accepted J. Math Physics.
- A Numerical Algorithm for the 2D Autoregressive Filter Problem"
(with H. Woerdeman and G. Castro) Accepted IEEE Transactions in Signal Proc.
- Certain Two Dimensional Integrals that Appear in Conformal Field Theory"
(with H. Navelet) Accepted J. Math Physics.
- Positive
Extensions, Fejer-Riesz Factorization and Autoregressive Filters in Two Variables
(pdf version for downloading)(with Hugo Woerdeman) Accepted Annals of Math.
- Squeezable
orthogonal bases: Accuracy and Smoothness(pdf version)(with George
Donovan and Doug Hardin) SINUM 40 (2002),1077-1099
-
Squeezable orthogonal bases, and adaptive least squares
(postscript version for downloading)(with G.C. Donovan, D.P. Hardin,
P. Massopust) Wavelet Applications in Signal and
Image Processing}, Aldroubi, Laine & Unser, SPIE conf. Proc.,
San Diego 1997.
-
An Inverse Problem Associated with Polynomials Orthogonal on the
Unit Circle(postscript version for downloading)(with R. Johnson)
CMP
- Construction of
Orthogonal Wavelets Using Fractal Interpolation Functions
(postscript version for downloading)(with G.C. Donovan, D.P. Hardin,
P. Massopust) SIAM J. Math. Anal 27,(1996),1158-1192
- Intertwining
multiresolution analysis and the construction of piecewise polynomial
wavelets(postscript version for downloading)(with G.C. Donovan, and
D.P. Hardin), SIAM J. Math Anal. 27,(1996), 1791-1815
- Orthogonal
Polynomials and the construction of piecewise polynomial
smooth wavelets(postscript version for downloading)
(with G.C. Donovan, D.P. Hardin), SIAM J. Math Anal. 30, (1998),1029-1056
-
Compactly Supported, Piecewise Affine Scaling Functions on
Triangulations(postscript version for downloading)
(with G.C. Donovan, D.P. Hardin), Const. Approx. 16,(2000),201-219
- Rotation Number associated with polynomials orthogonal on the unit
circle(with Russel Johnson) J. DIF. EQ. 132,(1996),140-178
Courses:
Updated Jan 2003
