Seminars and Colloquia by Series

Hardy Space Theory on Product Spaces of Homogeneous Type Via Orthonormal Wavelet Bases

Series
Analysis Seminar
Time
Thursday, April 10, 2014 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ji Li – Macquarie University, Sydney, Australia
We study Hardy spaces on spaces X which are the n-fold product of homogeneous spaces. An important tool is the remarkable orthonormal wavelet basis constructed Hytonen. The main tool we develop is the Littlewood-Paley theory on X, which in turn is a consequence of a corresponding theory on each factor space. We make no additional assumptions on the quasi-metric or the doubling measure for each factor space, and thus we extend to the full generality of product spaces of homogeneous type the aspects of both one-parameter and multiparameter theory involving Littlewood-Paley theory and function spaces. Moreover, our methods would be expected to be a powerful tool for developing function spaces and the boundedness of singular integrals on spaces of homogeneous type. This is joint work with Yongsheng Han and Lesley Ward.

KP hierarchy for the cyclic quiver

Series
Analysis Seminar
Time
Wednesday, April 9, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Oleg Chalykh – University of Leeds
I will discuss a generalization of the KP hierarchy, which is intimately related to the cyclic quiver and the Calogero-Moser problem for the wreath-product Sn≀Z/mZ.

Generalizations of Wermer's maximality theorem

Series
Analysis Seminar
Time
Wednesday, March 26, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alex Izzo – Bowling Green State University
A classical theorem of John Wermer asserts that the algebra of continuous functions on the circle with holomophic extensions to the disc is a maximal subalgebra of the algebra of all continuous functions on the circle. Wermer's theorem has been extended in numerous directions. These will be discussed with an emphasis on extensions to several complex variables.

Vector-valued inequalities with applications to bi-parameter problems.

Series
Analysis Seminar
Time
Wednesday, March 12, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prabath Silva – Indiana University
In this talk we will discuss applications of a new method of proving vector-valued inequalities discovered by M. Bateman and C. Thiele. We give new proofs of the Fefferman-Stein inequality (without using weighted theory) and vector-valued estimates of the Carleson operator using this method. Also as an application to bi-parameter problems, we give a new proof for bi-parameter multipliers without using product theory. As an application to the bilinear setting, we talk about new vector-valued estimates for the bilinear Hilbert transform, and estimates for the paraproduct tensored with the bilinear Hilbert transform. The first part of this work is joint work with Ciprian Demeter.

A new type of exceptional Laguerre polynomials

Series
Analysis Seminar
Time
Monday, March 10, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Conni Liaw – Baylor University
The Bochner Classification Theorem (1929) characterizes the polynomial sequences {pn}∞n=0, with degpn=n that simultaneously form a complete set of eigenstates for a second order differential operator and are orthogonal with respect to a positive Borel measure having finite moments of all orders: Hermite, Laguerre, Jacobi and Bessel polynomials. In 2009, G\'{o}mez-Ullate, Kamran, and Milson found that for sequences {pn}∞n=1, with degpn=n (i.e.~without the constant polynomial) the only such sequences are the \emph{exceptional} Laguerre and Jacobi polynomials. They also studied two Types of Laguerre polynomial sequences which omit m polynomials. We show the existence of a new "Type III" family of Laguerre polynomials and focus on its properties.

Carleson and Reverse Carleson measures

Series
Analysis Seminar
Time
Wednesday, February 5, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bill Ross – University of Richmond
This will be a survey talk on the ongoing classification problem for Carleson and reverse Carleson measures for the de Branges-Rovnyak spaces. We will relate these problems to some recent work of Lacey and Wick on the boundedness of the Cauchy transform operator.

Universality in Random Normal Matrices

Series
Analysis Seminar
Time
Wednesday, January 22, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Roman Riser – ETH, Zurich
In the beginning, the basics about random matrix models and some facts about normal random matrices in relation with conformal map- pings will be explained. In the main part we will show that for Gaussian random normal matrices the eigenvalues will fill an elliptically shaped do- main with constant density when the dimension n of the matrices tends to infinity. We will sketch a proof of universality, which is based on orthogonal polynomials and an identity which plays a similar role as the Christoffel- Darboux formula in Hermitian random matrices. Especially we are interested in the density at the boundary where we scale the coordinates with n^(-1/2). We will also consider the off-diagonal part of the kernel and calculate the correlation function. The result will be illustrated by some graphics.

TBA by Alden Waters

Series
Analysis Seminar
Time
Wednesday, January 8, 2014 - 15:04 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alden Water – Univesity of Paris

The Cluster Value Problem for Banach Spaces

Series
Analysis Seminar
Time
Wednesday, November 20, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Sofia Ortega Castillo – Texas A&M University
I will introduce the cluster value problem, and its relation to the Corona problem, in the setting of Banach algebras of analytic functions on unit balls. Then I will present a reduction of the cluster value problem in separable Banach spaces, for the algebras Au and H∞, to those spaces that are ℓ1 sums of a sequence of finite dimensional spaces. This is joint work with William B. Johnson.

Landau's Density Results Revisited

Series
Analysis Seminar
Time
Wednesday, November 13, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Shahaf Nitzan – Kent State
This talk discusses exponential frames and Riesz sequences in L^2 over a set of finite measure. (Roughly speaking, Frames and Riesz sequences are over complete bases and under complete bases, respectively). Intuitively, one would assume that the frequencies of an exponential frame can not be too sparse, while those of an exponential Riesz sequence can not be too dense. This intuition was confirmed in a very general theorem of Landau, which holds for all bounded sets of positive measure. Landau's proof involved a deep study of the eigenvalues of compositions of certain projection operators. Over the years Landaus technique, as well as some relaxed version of it, were used in many different setting to obtain results of a similar nature. Recently , joint with A. Olevskii, we found a surprisingly simple approach to Landau's density theorems, which provides stronger versions of these results. In particular, the theorem for Riesz sequences was extended to unbounded sets (for frames, such an extension is trivial). In this talk we will discuss Landau's results and our approach for studying questions of this type.

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