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Generalized p-Adic Fourier Transform and Estimates of Integral Modulus of Continuity in Terms of This Transform

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Abstract

We consider a new class of functions on the p-adic linear space ℚ n p for which a Fourier transform can be defined.We prove equalities of Parseval type, an inversion formula and a sufficient condition for a function to be represented as this Fourier transform. Also we give a sharp estimate of the L2(ℚ n p ) modulus of continuity in terms of Fourier transform generalizing the result of S. S. Platonov in the case n = 1. Finally we prove a generalization of this result and its converse for Lq(ℚ n p ) with appropriate q.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Saratov State University, Astrakhanskaya Str. 83, 410012, Saratov, Russia

    S. S. Volosivets & M. A. Kuznetsova

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  1. S. S. Volosivets
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  2. M. A. Kuznetsova
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Correspondence to S. S. Volosivets.

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The text was submitted by the authors in English.

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Volosivets, S.S., Kuznetsova, M.A. Generalized p-Adic Fourier Transform and Estimates of Integral Modulus of Continuity in Terms of This Transform. P-Adic Num Ultrametr Anal Appl 10, 312–321 (2018). https://doi.org/10.1134/S2070046618040088

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  • DOI: https://doi.org/10.1134/S2070046618040088

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