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Sibirsk. Mat. Zh., 2009, Volume 50, Number 1, Pages 3–18 (Mi smj1932)  

This article is cited in 1 scientific paper (total in 1 paper)

Applications of $\mathbf P$-adic generalized functions and approximations by a system of $\mathbf P$-adic translations of a function

S. S. Volosivets

Saratov State University named after N. G. Chernyshevsky, Faculty of Mathematics and Mechanics

Abstract: Under some conditions we prove that the convergence of a sequence of functions in the space of $\mathbf P$-adic generalized functions is equivalent to its convergence in the space of locally integrable functions. Some analogs are established of the Wiener tauberian theorem and the Wiener theorem on denseness of translations for $\mathbf P$-adic convolutions and translations.

Keywords: $\mathbf P$-adic generalized function, $L_\mathrm{loc}^p(\mathbb R_+)$, multiplicative Fourier transform, Lebesgue points of order $p$, Wiener tauberian theorem, Wiener theorem on denseness of translations.

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English version:
Siberian Mathematical Journal, 2009, 50:1, 1–13

Bibliographic databases:

UDC: 517.51
Received: 31.08.2007

Citation: S. S. Volosivets, “Applications of $\mathbf P$-adic generalized functions and approximations by a system of $\mathbf P$-adic translations of a function”, Sibirsk. Mat. Zh., 50:1 (2009), 3–18; Siberian Math. J., 50:1 (2009), 1–13

Citation in format AMSBIB
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\by S.~S.~Volosivets
\paper Applications of $\mathbf P$-adic generalized functions and approximations by a~system of $\mathbf P$-adic translations of a~function
\jour Sibirsk. Mat. Zh.
\yr 2009
\vol 50
\issue 1
\pages 3--18
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\elib{https://elibrary.ru/item.asp?id=13601024}
\transl
\jour Siberian Math. J.
\yr 2009
\vol 50
\issue 1
\pages 1--13
\crossref{https://doi.org/10.1007/s11202-009-0001-z}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. A. Karapetyants, V. Yu. Protasov, “O prostranstvakh dvoichno-obobschennykh funktsii”, Funkts. analiz i ego pril., 54:4 (2020), 56–63  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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