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<p>The paper presents new connections between Wiener Banach algebras of absolutely convergent Fourier integrals of complex-valued Borel measures and various issues in the theory of Fourier series and integrals, as outlined in the classical monographs by Zygmund [<CitationRef CitationID="CR1">1</CitationRef>], Bary [<CitationRef CitationID="CR2">2</CitationRef>], and Stein–Weiss [<CitationRef CitationID="CR3">3</CitationRef>]. This two-way connection allows, in particular, deriving new properties of trigonometric Fourier series from the properties of Wiener algebras, and deriving new results about these algebras from known results on Fourier series.</p>

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On Trigonometric Fourier Series and Wiener Algebras

  • 期刊论文

  • 发表日期：

    2026年3月20日

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  • Roald M. Trigub

摘要

The paper presents new connections between Wiener Banach algebras of absolutely convergent Fourier integrals of complex-valued Borel measures and various issues in the theory of Fourier series and integrals, as outlined in the classical monographs by Zygmund [1], Bary [2], and Stein–Weiss [3]. This two-way connection allows, in particular, deriving new properties of trigonometric Fourier series from the properties of Wiener algebras, and deriving new results about these algebras from known results on Fourier series.