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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2011, Volume 90, Issue 4, Pages 541–557 (Mi mz8631)  

This article is cited in 5 scientific papers (total in 5 papers)

Haar System on the Product of Groups of $p$-Adic Integers

S. F. Lukomskii

Saratov State University named after N. G. Chernyshevsky

Abstract: We present an algorithm for constructing dilation operators on the product of groups of $p$-adic integers and construct a system of Haar functions which is obtained from a single function by using the operations of contraction, translation, and raising to a power. In the two-dimensional case, we describe all the Haar bases.

Keywords: system of Haar functions, the group of $p$-adic integers, wavelet basis, Haar basis, compact group, quotient group, Rademacher function, dilation operator, cyclic subgroup, coset

DOI: https://doi.org/10.4213/mzm8631

Full text: PDF file (574 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2011, 90:4, 517–532

Bibliographic databases:

UDC: 517.51
Received: 16.12.2009
Revised: 08.11.2010

Citation: S. F. Lukomskii, “Haar System on the Product of Groups of $p$-Adic Integers”, Mat. Zametki, 90:4 (2011), 541–557; Math. Notes, 90:4 (2011), 517–532

Citation in format AMSBIB
\Bibitem{Luk11}
\by S.~F.~Lukomskii
\paper Haar System on the Product of Groups of~$p$-Adic Integers
\jour Mat. Zametki
\yr 2011
\vol 90
\issue 4
\pages 541--557
\mathnet{http://mi.mathnet.ru/mz8631}
\crossref{https://doi.org/10.4213/mzm8631}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2962211}
\transl
\jour Math. Notes
\yr 2011
\vol 90
\issue 4
\pages 517--532
\crossref{https://doi.org/10.1134/S0001434611090239}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000296476500023}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80155142556}


Linking options:
  • http://mi.mathnet.ru/eng/mz8631
  • https://doi.org/10.4213/mzm8631
  • http://mi.mathnet.ru/eng/mz/v90/i4/p541

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Lukomskii S.F., “Haar system on a product of zero-dimensional compact groups”, Cent. Eur. J. Math., 9:3 (2011), 627–639  crossref  mathscinet  zmath  isi  elib  scopus
    2. I. Ya. Novikov, M. A. Skopina, “Why Are Haar Bases in Various Structures the Same?”, Math. Notes, 91:6 (2012), 895–898  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. Lukomskii S.F., “Multiresolution analysis on product of zero-dimensional Abelian groups”, J. Math. Anal. Appl., 385:2 (2012), 1162–1178  crossref  mathscinet  zmath  isi  elib  scopus
    4. S. F. Lukomskii, “Matrichnoe predstavlenie operatora rastyazheniya v proizvedenii lokalno-kompaktnykh nul-mernykh grupp”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 13:2(1) (2013), 8–14  mathnet  crossref
    5. Evdokimov S., “On non-compactly supported p-adic wavelets”, J. Math. Anal. Appl., 443:2 (2016), 1260–1266  crossref  mathscinet  zmath  isi  elib  scopus
  • Математические заметки Mathematical Notes
    Number of views:
    This page:446
    Full text:93
    References:70
    First page:19

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020