Time-Frequency Analysis Meets Operator Algebras

Keywords

Frames; Gabor representations; Group representations; Operator algebras; Time-frequency analysis

Abstract

There are several well-known fundamental theorems in Gabor analysis that are naturally connected to group representation theory and theory of operator algebras. While some of these connections between time-frequency analysis and operator algebras were established by Jon von Neumann in 1930s, they have been extensively investigated more recently mainly due to the developments of wavelet/Gabor theory, or more generally, the theory of frames in the last two decades. In this article, we will discuss some of the main results we obtained in the last few years together with some new results, exposition and open problems. We will be mainly focused on the results that were originated from time-frequency analysis but reflect intrinsic connections with group representation theory. In particular, we give a detailed account on an abstract version of the duality principle in time-frequency analysis for group representations, and its connections with some open problems in the theory of operator algebras.

Publication Date

1-1-2017

Publication Title

Acta Mathematica Sinica, Chinese Series

Volume

60

Issue

1

Number of Pages

3-18

Document Type

Article

Personal Identifier

scopus

Socpus ID

85020755034 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85020755034

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