RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






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


Tr. Mat. Inst. Steklova, 2010, Volume 269, Pages 8–30 (Mi tm2904)  

This article is cited in 8 scientific papers (total in 8 papers)

Wavelet approximation and Fourier widths of classes of periodic functions of several variables. I

D. B. Bazarkhanov

Institute of Mathematics, Almaty, Kazakhstan

Abstract: We obtain characterizations (and prove the corresponding equivalence of norms) of function spaces $\mathbf B^{sm}_{pq}(\mathbb I^k)$ and $\mathbf L^{sm}_{pq}(\mathbb I^k)$ of Nikol'skii–Besov and Lizorkin–Triebel types, respectively, in terms of representations of functions in these spaces by Fourier series with respect to a multiple system $\mathcal W^\mathbb I_m$ of Meyer wavelets and in terms of sequences of the Fourier coefficients with respect to this system. We establish order-sharp estimates for the approximation of functions in $B^{sm}_{pq}(\mathbb I^k)$ and $L^{sm}_{pq}(\mathbb I^k)$ by special partial sums of these series in the metric of $L_r(\mathbb I^k)$ for a number of relations between the parameters $s,p,q,r$, and $m$ ($s=(s_1,…,s_n)\in\mathbb R^n_+$, $1\leq p,q,r\leq\infty$, $m=(m_1,…,m_n)\in\mathbb N^n$, $k=m_1+…+m_n$, and $\mathbb I= \mathbb R$ or $\mathbb T$). In the periodic case, we study the Fourier widths of these function classes.

Full text: PDF file (341 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 269, 2–24

Bibliographic databases:

Document Type: Article
UDC: 517.518.224+517.518.837
Received in January 2010

Citation: D. B. Bazarkhanov, “Wavelet approximation and Fourier widths of classes of periodic functions of several variables. I”, Function theory and differential equations, Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday, Tr. Mat. Inst. Steklova, 269, MAIK Nauka/Interperiodica, Moscow, 2010, 8–30; Proc. Steklov Inst. Math., 269 (2010), 2–24

Citation in format AMSBIB
\Bibitem{Baz10}
\by D.~B.~Bazarkhanov
\paper Wavelet approximation and Fourier widths of classes of periodic functions of several variables.~I
\inbook Function theory and differential equations
\bookinfo Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2010
\vol 269
\pages 8--30
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm2904}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2729970}
\zmath{https://zbmath.org/?q=an:1219.42025}
\elib{http://elibrary.ru/item.asp?id=15109748}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2010
\vol 269
\pages 2--24
\crossref{https://doi.org/10.1134/S0081543810020021}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000281705900002}
\elib{http://elibrary.ru/item.asp?id=15367530}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77956636115}


Linking options:
  • http://mi.mathnet.ru/eng/tm2904
  • http://mi.mathnet.ru/eng/tm/v269/p8

    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. D. B. Bazarkhanov, “Estimates for the widths of classes of periodic functions of several variables – I”, Eurasian Math. J., 1:3 (2010), 11–26  mathnet  mathscinet  zmath
    2. Hansen M. Sickel W., “Best M-Term Approximation and Sobolev-Besov Spaces of Dominating Mixed Smoothness-the Case of Compact Embeddings”, Constr. Approx., 36:1 (2012), 1–51  crossref  mathscinet  zmath  isi  elib  scopus
    3. Bazarkhanov D.B., “Wavelet Approximation and Fourier Widths of Classes of Periodic Functions of Several Variables. II”, Anal. Math., 38:4 (2012), 249–289  crossref  mathscinet  zmath  isi
    4. D. B. Bazarkhanov, “Nonlinear approximations of classes of periodic functions of many variables”, Proc. Steklov Inst. Math., 284 (2014), 2–31  mathnet  crossref  crossref  isi
    5. Sh. A. Balgimbaeva, T. I. Smirnov, “Otsenki poperechnikov Fure klassov periodicheskikh funktsii so smeshannym modulem gladkosti”, Tr. IMM UrO RAN, 21, no. 4, 2015, 78–94  mathnet  mathscinet  elib
    6. D. B. Bazarkhanov, “Nonlinear trigonometric approximations of multivariate function classes”, Proc. Steklov Inst. Math., 293 (2016), 2–36  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Balgimbayeva Sh.A., “Hyperbolic Cross Approximation With Respect to Wavelet System With Compact Supports”, International Conference Functional Analysis in Interdisciplinary Applications (FAIA2017), AIP Conference Proceedings, 1880, eds. Kalmenov T., Sadybekov M., Amer Inst Physics, 2017, UNSP 030005  crossref  mathscinet  isi  scopus
    8. D. B. Bazarkhanov, “Lineinoe vosstanovlenie psevdodifferentsialnykh operatorov na klassakh gladkikh funktsii na m-mernom tore. I”, Tr. IMM UrO RAN, 24, no. 4, 2018, 57–79  mathnet  crossref  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:330
    Full text:9
    References:88

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