Email this article Generalized p-Adic Fourier Transform and Estimates of Integral Modulus of Continuity in Terms of This Transform
- Authors: Volosivets S.S.1, Kuznetsova M.A.1
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Affiliations:
- Faculty of Mechanics and Mathematics
- Issue: Vol 10, No 4 (2018)
- Pages: 312-321
- Section: Research Articles
- URL: https://journals.rcsi.science/2070-0466/article/view/201102
- DOI: https://doi.org/10.1134/S2070046618040088
- ID: 201102
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Abstract
We consider a new class of functions on the p-adic linear space ℚpn 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(ℚpn) 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(ℚpn) with appropriate q.
About the authors
S. S. Volosivets
Faculty of Mechanics and Mathematics
Author for correspondence.
Email: volosivetsss@mail.ru
Russian Federation, Astrakhanskaya Str. 83, Saratov, 410012
M. A. Kuznetsova
Faculty of Mechanics and Mathematics
Email: volosivetsss@mail.ru
Russian Federation, Astrakhanskaya Str. 83, Saratov, 410012
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