Izvestiya: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izvestiya: Mathematics, 2005, Volume 69, Issue 2, Pages 221–263
DOI: https://doi.org/10.1070/IM2005v069n02ABEH000529
(Mi im632)
 

This article is cited in 7 scientific papers (total in 7 papers)

Non-linear singular problems in $p$-adic analysis: associative algebras of $p$-adic distributions

S. A. Albeverio, A. Yu. Khrennikov, V. M. Shelkovich
References:
Abstract: We propose an algebraic theory which can be used for solving both linear and non-linear singular problems of $p$-adic analysis related to $p$-adic distributions (generalized functions). We construct the $p$-adic Colombeau–Egorov algebra of generalized functions, in which Vladimirov's pseudo-differential operator plays the role of differentiation. This algebra is closed under Fourier transformation and associative convolution. Pointvalues of generalized functions are defined, and it turns out that any generalized function is uniquely determined by its pointvalues. We also construct an associative algebra of asymptotic distributions, which is generated by the linear span of the set of associated homogeneous $p$-adic distributions. This algebra is embedded in the Colombeau–Egorov algebra as a subalgebra. In addition, a new technique for constructing weak asymptotics is developed.
Received: 04.06.2004
Bibliographic databases:
UDC: 517.982.4+511.225
MSC: Primary 46F30, 11F88; Secondary 46F10, 22E50
Language: English
Original paper language: Russian
Citation: S. A. Albeverio, A. Yu. Khrennikov, V. M. Shelkovich, “Non-linear singular problems in $p$-adic analysis: associative algebras of $p$-adic distributions”, Izv. Math., 69:2 (2005), 221–263
Citation in format AMSBIB
\Bibitem{AlbKhrShe05}
\by S.~A.~Albeverio, A.~Yu.~Khrennikov, V.~M.~Shelkovich
\paper Non-linear singular problems in $p$-adic analysis: associative algebras of $p$-adic distributions
\jour Izv. Math.
\yr 2005
\vol 69
\issue 2
\pages 221--263
\mathnet{http://mi.mathnet.ru//eng/im632}
\crossref{https://doi.org/10.1070/IM2005v069n02ABEH000529}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2136256}
\zmath{https://zbmath.org/?q=an:1096.46041}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000230436900001}
\elib{https://elibrary.ru/item.asp?id=9176276}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-31144447274}
Linking options:
  • https://www.mathnet.ru/eng/im632
  • https://doi.org/10.1070/IM2005v069n02ABEH000529
  • https://www.mathnet.ru/eng/im/v69/i2/p3
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024