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In this chapter inversion formulas are proven which provide the inverse of the Fourier transform of measures so that one can reconstruct from the Fourier transform the measure and possibly a density. After this investigation the Bochner-Khinchin theorem is verified by which one can deduce the existence of certain fundamental probability measures.

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Fourier Inversion Formulas

  • 章节

  • 发表日期：

    2025年

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  • Hannah Geiss,
  • Stefan Geiss

摘要

In this chapter inversion formulas are proven which provide the inverse of the Fourier transform of measures so that one can reconstruct from the Fourier transform the measure and possibly a density. After this investigation the Bochner-Khinchin theorem is verified by which one can deduce the existence of certain fundamental probability measures.