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<p>We establish a general form of Wiener’s lemma for measures on locally compact Abelian groups by using Fourier analysis and the theory of Følner sequences. Our approach provides a unified framework that encompasses both the discrete and continuous cases. We also show a version of Wiener’s lemma for Bochner–Riesz means on both <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb {R}}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\mathbb {T}}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">T</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation>.</p>

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On Wiener’s lemma on locally compact Abelian groups

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Philippe Jaming,
  • Karim Kellay,
  • Rolando Perez III

摘要

We establish a general form of Wiener’s lemma for measures on locally compact Abelian groups by using Fourier analysis and the theory of Følner sequences. Our approach provides a unified framework that encompasses both the discrete and continuous cases. We also show a version of Wiener’s lemma for Bochner–Riesz means on both \({\mathbb {R}}^d\) R d and \({\mathbb {T}}^d\) T d .