Spectral Invariance of Quasi-Banach Algebras for Matrices and Pseudodifferential Operators

TL;DR

This paper extends the spectral invariance property of pseudodifferential operators to a broader class of modulation spaces with Lebesgue exponents less than one, relevant in approximation and data compression.

Contribution

It generalizes spectral invariance results to quasi-Banach modulation spaces with smaller Lebesgue exponents, expanding applicability.

Findings

Spectral invariance holds for a wider class of modulation spaces.

Applicable to approximation theory and data compression.

Extends previous results to non-weighted spaces.

Abstract

In the paper we extend the spectral invariance of pseudodifferential operators acting on (non-weighted) classical modulation spaces to allow the Lebesgue exponents to be smaller than one. These spaces occur naturally in approximation theory and data compression problems.