Seminars and Colloquia by Series

Solvable Schroedinger equations with trigonometric potentials: From quantum $A_N$ (Sutherland to $E_8$ trigonometric models

Series
Analysis Seminar
Time
Wednesday, October 10, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alexander Turbiner – Nuclear Science Institute, UNAM, Mexico
A brief overview of some integrable and exactly-solvable Schroedinger equations with trigonometric potentials of Calogero-Moser-Sutherland type is given.All of them are characterized bya discrete symmetry of the Hamiltonian given by the affine Weyl group,a number of polynomial eigenfunctions and eigenvalues which are usually quadratic in the quantum number, each eigenfunction is an element of finite-dimensionallinear space of polynomials characterized by the highest root vector, anda factorization property for eigenfunctions. They admitan algebraic form in the invariants of a discrete symmetry group(in space of orbits) as 2nd order differential operator with polynomial coefficients anda hidden algebraic structure. The hidden algebraic structure for $A-B-C-D$-series is related to the universal enveloping algebra $U_{gl_n}$. For the exceptional $G-F-E$-seriesnew infinite-dimensional finitely-generated algebras of differential operatorswith generalized Gauss decomposition property occur.

C*-algebras Generated by Composition Operators

Series
Analysis Seminar
Time
Wednesday, October 3, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Katie Quertermous – James Madison University
In this talk, we investigate the structures of C*-algebras generated by collections of linear-fractionally-induced composition operators and either the forward shift or the ideal of compact operators. In the setting of the classical Hardy space, we present a full characterization of the structures, modulo the ideal of compact operators, of C*-algebras generated by a single linear-fractionally-induced composition operator and the forward shift. We apply the structure results to compute spectral information for algebraic combinations of composition operators. We also discuss related results for C*-algebras of operators on the weighted Bergman spaces.

Nonlinear transformations of moment sequences

Series
Analysis Seminar
Time
Wednesday, September 12, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Antonio Duran – University of Seville
In this talk we discuss some nonlinear transformations between moment sequences. One of these transformations is the following: if (a_n)_n is a non-vanishing Hausdorff moment sequence then the sequence defined by 1/(a_0 ... a_n) is a Stieltjes moment sequence. Our approach is constructive and use Euler's idea of developing q-infinite products in power series. Some others transformations will be considered as well as some relevant moment sequences and analytic functions related to them. We will also propose some conjectures about moment transformations defined by means of continuous fractions.

Similarity results for operators of class C_0

Series
Analysis Seminar
Time
Wednesday, September 5, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Raphael Clouatre – Indiana University
The classification theorem for a C_0 operator describes its quasisimilarity class by means of its Jordan model. The purpose of this talk will be to investigate when the relation between the operator and its model can be improved to similarity. More precisely, when the minimal function of the operator T can be written as a product of inner functions satisfying the so-called (generalized) Carleson condition, we give some natural operator theoretic assumptions on T that guarantee similarity.

Uchiyama's lemma and the John-Nirenberg inequality

Series
Analysis Seminar
Time
Wednesday, August 29, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Greg Knese – University of Alabama
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.

About polynomially bounded operators and invariant subspaces

Series
Analysis Seminar
Time
Friday, May 4, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor Bernard Chevreau – University of Bordeaux 1
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.

Regularity of solutions to degenerate p-Laplace equations

Series
Analysis Seminar
Time
Wednesday, April 25, 2012 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Kabe Moen – University of Alabama
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.

On W. Rudin's problem

Series
Analysis Seminar
Time
Wednesday, April 25, 2012 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Konstantin Oskolkov – University of South Carolina

Agler Decompositions on the Bidisk

Series
Analysis Seminar
Time
Wednesday, April 18, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Kelly Bickel – Washington University - St. Louis
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.

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