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# Archive : Inverse Problems and Analysis

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 Professor Hartmut Fuhr, RWTH Aachen University, Germany 143 Professor Hartmut Fuhr, RWTH Aachen University, Germany Zoom

​​Attend this seminar via Zoom​. ​

Title: Coarse geometric methods for generalized wavelet approximation theory

Abstract: Generalized wavelet systems in higher dimensions arise from the action of suitable semidirect products $\mathbb{R}^d \rtimes H$ on ${\rm L}^2(\mathbb{R}^d)$. Here $H$ denotes a suitably chosen matrix group acting on functions by dilations. The approximation theoretic properties of these systems are coded in the associated {\em coorbit spaces}, defined by imposing suitably weighted $L^p$-norms on the transform side. Understanding the dependence of the scale of coorbit spaces on the dilation group is one of the basic problems of the theory, and generally not well understood.

The talk translates this question into a problem from the domain of coarse geometry. Under suitable technical assumptions on two dilation groups $H_1,H_2$, the dual action of these groups induces a map $\varphi: H_1 \to H_2$, and it can be shown that $H_1$ and $H_2$ have the same scale of coorbit spaces if and only if $\varphi$ is a quasi-isometry with respect to word metrics defined on $H_1$ and $H_2$.

As an application of this method, we present a classification result for so-called generalized shearlet dilation groups in arbitrary dimensions.

(Based on joint work with Rene Koch.)​

11/16/2021 8:30:00 PM 11/16/2021 9:30:00 PM Professor Elias Katsoulis, East Carolina University 142 Professor Elias Katsoulis, East Carolina University In-person talk at EWG 336

Title: The isomorphism problem for tensor algebras of C*-correspondences.

Abstract: The tensor algebras of C*-correspondences include as motivating examples the semicrossed products, the graph algebras and various other algebras. In this talk we will be concerned with the isomorphism problem between such algebras. We will review some old work and present some recent developments obtained jointly with Chris Ramsey.

10/26/2021 7:30:00 PM 10/26/2021 8:30:00 PM Dr. Yemon Choi, Lancaster University, UK 141 Dr. Yemon Choi, Lancaster University, UK Zoom

​​Attend this seminar via Zoom​. ​

Title: Operator space tensor products, and cocycles on Fourier algebras

Abstract: When studying Fourier algebras of locally compact groups, it is commonly accepted that we need to use the projective tensor product of operator spaces. On the other hand, the study of derivations on Fourier algebras has revealed a potentially rich area for investigation, but such derivations can never be completely bounded, and hence there would seem to be no reason why they should interact well with operator space tensor products.

In this talk I will explain more about these two themes, and why they presented an obstacle until recently when trying to construct non-trivial 2-cocycles on Fourier algebras. I will then outline how the obstacle can be overcome by making use of extra structure for certain derivations, together with a "twisted inclusion" result for operator space tensor products.

10/19/2021 7:30:00 PM 10/19/2021 8:30:00 PM Professor Qiyu Sun, University of Central Florida 140 Professor Qiyu Sun, University of Central Florida Zoom Title: Polynomial filters of multiple commutative shifts and their distributed implementation

Abstract: Graph signal processing provides an innovative framework to handle data residing on distributed networks. Polynomial graph filters and their inverses play important roles in graph signal processing. The concept of commutative graph shifts plays a similar role in graph signal processing as the one-order delay in classical multi-dimensional signal processing. In this talk, we consider the filtering and inverse filtering procedure associated polynomial filters of multiple commutative shifts. We also consider iterative approximation algorithms and the associated distributed optimization problems.​​

Attend this seminar via Zoom​

10/5/2021 7:30:00 PM 10/5/2021 8:30:00 PM

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