## Seminars and Colloquia by Series

Wednesday, August 29, 2012 - 14:00 , Location: Skiles 005 , Greg Knese , University of Alabama , Organizer: Jeff Geronimo
Using integral formulas based on Green's theorem and in particular a lemma of Uchiyama, we give simple proofs of comparisons of different BMO norms without using the John-Nirenberg inequality while we also give a simple proof of the strong John-Nirenberg inequality. Along the way we prove the inclusions of BMOA in the dual of H^1 and BMO in the dual of real H^1. Some difficulties of the method and possible future directions to take it will be suggested at the end.
Friday, May 4, 2012 - 11:00 , Location: Skiles 006 , Professor Bernard Chevreau , University of Bordeaux 1 , Organizer:
In the first part of the talk we will give a brief survey of significant results going from S. Brown pioneering work showing the existence of invariant subspaces for subnormal operators (1978) to Ambrozie-Muller breakthrough asserting the same conclusion for the adjoint of a polynomially bounded operator (on any Banach space) whose spectrum contains the unit circle (2003). The second part will try to give some insight of the different techniques involved in this series of results, culminating with a brilliant use of Carleson interpolation theory for the last one. In the last part of the talk we will discuss additional open questions which might be investigated by these techniques.
Wednesday, April 25, 2012 - 15:30 , Location: Skiles 005 , Kabe Moen , University of Alabama , Organizer: Michael Lacey
Motivated by mappings of finite distortion, we consider degenerate p-Laplacian equations whose ellipticity condition is satisfied by thedistortion tensor and the inner distortion function of such a mapping. Assuming a certain Muckenhoupt type condition on the weightinvolved in the ellipticity condition, we describe the set of continuity of solutions.
Wednesday, April 25, 2012 - 15:30 , Location: Skiles 005 , Konstantin Oskolkov , University of South Carolina , Organizer: Michael Lacey
Wednesday, April 18, 2012 - 14:00 , Location: Skiles 005 , Kelly Bickel , Washington University - St. Louis , Organizer:
It is well-known that every Schur function on the bidisk can be written as a sum involving two positive semidefinite kernels. Such decompositions, called Agler decompositions, have been used to answer interpolation questions on the bidisk as well as to derive the transfer function realization of Schur functions used in systems theory. The original arguments for the existence of such Agler decompositions were nonconstructive and the structure of these decompositions has remained quite mysterious. In this talk, we will discuss an elementary proof of the existence of Agler decompositions on the bidisk, which is constructive for inner functions. We will use this proof as a springboard to examine the structure of such decompositions and properties of their associated reproducing kernel Hilbert spaces.
Wednesday, April 11, 2012 - 14:00 , Location: Skiles 005 , Vladimir Eiderman , University of Wisconsin , Organizer: Michael Lacey
This is a joint work with F.~Nazarov and A.~Volberg.Let $s\in(1,2)$, and let $\mu$ be a finite positive Borel measure in $\mathbb R^2$ with $\mathcal H^s(\supp\mu)<+\infty$. We prove that if the lower $s$-density of $\mu$ is+equal to zero $\mu$-a.~e. in $\mathbb R^2$, then$\|R\mu\|_{L^\infty(m_2)}=\infty$, where $R\mu=\mu\ast\frac{x}{|x|^{s+1}}$ and $m_2$ is the Lebesque measure in $\mathbb R^2$. Combined with known results of Prat and+Vihtil\"a, this shows that for  any noninteger $s\in(0,2)$ and any finite positive Borel measure in $\mathbb R^2$ with $\mathcal H^s(\supp\mu)<+\infty$, we have+$\|R\mu\|_{L^\infty(m_2)}=\infty$.Also I will tell about the resent result of Ben Jaye, as well as about open problems.
Monday, March 26, 2012 - 14:00 , Location: Skiles 114 , Dan Timotin , Indiana University and Mathematical Institute of Romania , Organizer:
Truncated Toeplitz operators, introduced in full generality by Sarason a few years ago, are compressions of multiplication operators on H^2 to subspaces invariant to the adjoint of the shift. The talk will survey this newly developing area, presenting several of the basic results and highlighting some intriguing open questions.
Wednesday, March 14, 2012 - 14:00 , Location: Skiles 006 , Vygantas Paulauskas , Vilnius University , Organizer: Michael Lacey
In the talk some problems related with the famous Chernoff square root of n - lemma in the theory of approximation of some semi-groups of operators will be discussed. We present some optimal bounds in these approximations (one of them is Euler approximation) and two new classes of operators, generalizing sectorial and quasi-sectorial operators will be introduced. The talk is based on two papers [V. Bentkus and V. Paulauskas, Letters in Math. Physics, 68, (2004), 131-138] and [V. Paulauskas, J. Functional Anal., 262, (2012), 2074-2099]
Wednesday, March 7, 2012 - 14:00 , Location: Skiles 005 , Mark Lewko , University of Texas , Organizer: Michael Lacey
We will discuss several results (and open problems) related to rearrangements of Fourier series, particularly quantitative questions about maximal and variational operators. For instance, we show that the canonical ordering of the trigonometric system is not optimal for certain problems in this setting. Connections with analytic number theory will also be given. This is based on joint work with Allison Lewko.
Wednesday, February 22, 2012 - 14:00 , Location: Skiles 006 , Prof. Avram Sidi , Tecnion-IIT, Haifa, Israel , Organizer: Doron Lubinsky
We discuss some recent generalizations of Euler--Maclaurin expansions for the trapezoidal rule and of analogous asymptotic expansions for Gauss--Legendre quadrature, in the presence of arbitrary algebraic-logarithmic endpoint singularities. In addition of being of interest by themselves, these asymptotic expansions enable us to design appropriate variable transformations to improve the accuracies of these quadrature formulas arbitrarily. In general, these transformations are singular, and their singularities can be adjusted easily to achieve this improvement. We illustrate this issue with a numerical example involving Gauss--Legendre quadrature. We also discuss some recent asymptotic expansions of the coefficients of Legendre polynomial expansions of functions over a finite interval, assuming that the functions may have arbitrary algebraic-logarithmic interior and endpoint suingularities. These asymptotic expansions can be used to make definitive statements on the convergence acceleration rates of extrapolation methods as these are applied to the Legendre polynomial expansions.