Contemporary Mathematics. Fundamental Directions
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Publishing Ethics

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



CMFD:
Year:
Volume:
Issue:
Page:
Find






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


CMFD, 2007, Volume 25, Pages 58–79 (Mi cmfd106)  

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

On a Norm and Approximate Characteristics of Classes of Multivariable Functions

B. S. Kashina, V. N. Temlyakovb

a Steklov Mathematical Institute, Russian Academy of Sciences
b University of South Carolina

Abstract: We introduce a space of quasicontinuous functions and study its approximate characteristics, i.e., $\varepsilon$-entropy and widths. We establish inequalities for norms of trigonometric polynomials in this space. Besides, we obtain exponents of $\varepsilon$-entropy and widths of some classes of functions with low smoothness.

Full text: PDF file (274 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences, 2008, 155:1, 57–80

Bibliographic databases:

UDC: 517.5

Citation: B. S. Kashin, V. N. Temlyakov, “On a Norm and Approximate Characteristics of Classes of Multivariable Functions”, Theory of functions, CMFD, 25, PFUR, M., 2007, 58–79; Journal of Mathematical Sciences, 155:1 (2008), 57–80

Citation in format AMSBIB
\Bibitem{KasTem07}
\by B.~S.~Kashin, V.~N.~Temlyakov
\paper On a Norm and Approximate Characteristics of Classes of Multivariable Functions
\inbook Theory of functions
\serial CMFD
\yr 2007
\vol 25
\pages 58--79
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd106}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2342538}
\zmath{https://zbmath.org/?q=an:1167.26311}
\elib{https://elibrary.ru/item.asp?id=13597313}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 155
\issue 1
\pages 57--80
\crossref{https://doi.org/10.1007/s10958-008-9208-y}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-55749106743}


Linking options:
  • http://mi.mathnet.ru/eng/cmfd106
  • http://mi.mathnet.ru/eng/cmfd/v25/p58

    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. P. G. Grigor'ev, A. O. Radomskii, “Some Trigonometric Polynomials with Extremally Small Uniform Norm”, Math. Notes, 98:2 (2015), 230–236  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. O. Radomskii, “On approximation characteristics of some classes of functions of small smoothness”, Siberian Math. J., 59:3 (2018), 486–493  mathnet  crossref  crossref  mathscinet  isi  elib
    3. B. S. Kashin, Yu. V. Malykhin, K. S. Ryutin, “Kolmogorov width and approximate rank”, Proc. Steklov Inst. Math., 303 (2018), 140–153  mathnet  crossref  crossref  mathscinet  isi  elib
    4. V. N. Temlyakov, “Sampling Discretization of Integral Norms of the Hyperbolic Cross Polynomials”, Proc. Steklov Inst. Math., 312 (2021), 270–281  mathnet  crossref  crossref  isi  elib
  • Современная математика. Фундаментальные направления
    Number of views:
    This page:596
    Full text:203
    References:34

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021