A Fuglede type theorem for Fourier multiplier operators

Journal article (2022)

Authors

B. de Pagter Analysis - EEMCS
Werner J. Ricker Katholische Universität Eichstätt - Ingolstadt
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2022 B. de Pagter, Werner J. Ricker
DOI: https://doi.org/10.1016/j.indag.2022.10.005
Compact abelian group Fourier multiplier operator Reflection invariance Translation invariant Banach function space
More Info
expand_more

Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

Let E be a translation invariant Banach function space over an infinite compact abelian group G and Mφ be a Fourier multiplier operator (with symbol φ) acting on E. It is assumed that E has order continuous norm and that E is reflection invariant (which ensures that φ̄ is also a multiplier symbol for E). The following Fuglede type theorem is established. Whenever T is a bounded linear operator on E satisfying MφT=TMφ, then also Mφ̄T=TMφ̄.