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An Interplay of Multidimensional Variations in Fourier Analysis

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Abstract

We compare the Fourier integral of a function of bounded variation and the corresponding trigonometric series, generated by that function, in the multidimensional case. Several known notions of bounded variation are used and a new one is introduced. The obtained results are applied to integrability of multidimensional trigonometric series.

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Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, 52900, Ramat-Gan, Israel

    E. Liflyand

  2. Department of Mathematics, University of Ulm, 89069, Ulm, Germany

    U. Stadtmüller

  3. Department of Mathematics, Donetsk National University, 83055, Donetsk, Ukraine

    R. Trigub

Authors
  1. E. Liflyand
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  2. U. Stadtmüller
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  3. R. Trigub
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Corresponding author

Correspondence to E. Liflyand.

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Communicated by T. Körner.

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Liflyand, E., Stadtmüller, U. & Trigub, R. An Interplay of Multidimensional Variations in Fourier Analysis. J Fourier Anal Appl 17, 226–239 (2011). https://doi.org/10.1007/s00041-010-9136-3

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  • DOI: https://doi.org/10.1007/s00041-010-9136-3

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