RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Sibirsk. Mat. Zh.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (353 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.51

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
\Bibitem{Vol09} \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 \mathnet{http://mi.mathnet.ru/smj1932} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2502869} \elib{http://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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000263525700001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65149085232}