Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets

Krzysztof Nowak

ArticleOriginal scientific text

Title

Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets

Authors ¹

Affiliations

Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Abstract

We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions

g \mapsto P_{g, ϕ}

, where for a fixed function ϕ,

P_{g, ϕ}

denotes the one-dimensional orthogonal projection on the function

U_{g} ϕ

, U is a group representation and g is an element of the group. They are defined as integrals

ʃ_{W} P_{g, ϕ} d g

, where W is an open, relatively compact subset of a group. Our main result is a characterization of function spaces corresponding to local Toeplitz operators with pth power summable eigenvalues, 0 < p ≤ ∞.

Keywords

ENG

singular values, time-frequency localization

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Title

Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets

Affiliations

Abstract

Keywords

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