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In this chapter we study the Banach space of complex, Borel measures on the unit circle (endowed with the norm given by the total variation) in more detail. For this purpose we introduce the Fourier transform, Wiener’s lemma, and the related Koopmanvon Neumann lemma as fundamental and extremely powerful tools.

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Some Fourier Analysis

  • 章节

  • 发表日期：

    2025年

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  • Tanja Eisner,
  • Bálint Farkas

摘要

In this chapter we study the Banach space of complex, Borel measures on the unit circle (endowed with the norm given by the total variation) in more detail. For this purpose we introduce the Fourier transform, Wiener’s lemma, and the related Koopmanvon Neumann lemma as fundamental and extremely powerful tools.