A Fuglede type theorem for Fourier multiplier operators

Ben de Pagter, Werner J. Ricker

Research output: Contribution to journalArticleScientificpeer-review

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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.

Original languageEnglish
Pages (from-to)259-273
Number of pages15
JournalIndagationes Mathematicae
Volume34 (2023)
Issue number2
DOIs
Publication statusPublished - 2022

Keywords

  • Compact abelian group
  • Fourier multiplier operator
  • Reflection invariance
  • Translation invariant Banach function space

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