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, 2003, Volume 74, Issue 2, Pages 292–300 (Mi mz259)  

This article is cited in 4 scientific papers (total in 4 papers)

Polynomial Wavelet-Type Expansions on the Sphere

A. Askari-Hemmata, M. A. Dehghana, M. A. Skopinab

a Valiasr University
b Saint-Petersburg State University

Abstract: We present a polynomial wavelet-type system on $S^d$ such that any continuous function can be expanded with respect to these “wavelets”. The order of the growth of the degrees of the polynomials is optimal. The coefficients in the expansion are the inner products of the function and the corresponding element of a “dual wavelet system”. The “dual wavelets system” is also a polynomial system with the same growth of degrees of polynomials. The system is redundant. A construction of a polynomial basis is also presented. In contrast to our wavelet-type system, this basis is not suitable for implementation, because, first, there are no explicit formulas for the coefficient functionals and, second, the growth of the degrees of polynomials is too rapid.

DOI: https://doi.org/10.4213/mzm259

Full text: PDF file (221 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2003, 74:2, 278–285

Bibliographic databases:

UDC: 517.5
Received: 08.05.2002

Citation: A. Askari-Hemmat, M. A. Dehghan, M. A. Skopina, “Polynomial Wavelet-Type Expansions on the Sphere”, Mat. Zametki, 74:2 (2003), 292–300; Math. Notes, 74:2 (2003), 278–285

Citation in format AMSBIB
\Bibitem{AskDehSko03}
\by A.~Askari-Hemmat, M.~A.~Dehghan, M.~A.~Skopina
\paper Polynomial Wavelet-Type Expansions on the Sphere
\jour Mat. Zametki
\yr 2003
\vol 74
\issue 2
\pages 292--300
\mathnet{http://mi.mathnet.ru/mz259}
\crossref{https://doi.org/10.4213/mzm259}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2023771}
\zmath{https://zbmath.org/?q=an:1052.42027}
\elib{http://elibrary.ru/item.asp?id=13422021}
\transl
\jour Math. Notes
\yr 2003
\vol 74
\issue 2
\pages 278--285
\crossref{https://doi.org/10.1023/A:1025016510773}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000185172900032}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0346494533}


Linking options:
  • http://mi.mathnet.ru/eng/mz259
  • https://doi.org/10.4213/mzm259
  • http://mi.mathnet.ru/eng/mz/v74/i2/p292

    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. Fernandez NL, Prestin J, “Interpolatory band-limited wavelet bases on the sphere”, Constructive Approximation, 23:1 (2006), 79–101  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Feng, D, “Characterizations of function spaces on the sphere using frames”, Transactions of the American Mathematical Society, 359:2 (2007), 567  crossref  mathscinet  zmath  isi  scopus  scopus
    3. T. G. zhao, L. Naing, W. X. Yue, “Some New Features of the Boubaker Polynomials Expansion Scheme BPES”, Math. Notes, 87:2 (2010), 165–168  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Arfaoui S., Rezgui I., BenMabrouk A., “Wavelet Analysis on the Sphere: Spheroidal Wavelets”, Wavelet Analysis on the Sphere: Spheroidal Wavelets, Walter de Gruyter Gmbh, 2017, 1–144  mathscinet  isi
  • Математические заметки Mathematical Notes
    Number of views:
    This page:338
    Full text:90
    References:19
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019