Advertisement

Ukrainian Mathematical Journal

, Volume 54, Issue 5, pp 862–868 | Cite as

Trigonometric Widths of the Classes B p Ω of Periodic Functions of Many Variables

  • S. A. Stasyuk
Article

Abstract

We obtain exact order estimates for the trigonometric widths of the classes \(B_{p,{\theta }}^\Omega\) of periodic functions of many variables in the space Lq, 1 < p ≤ 2 ≤ q < p/(p − 1).

Keywords

Periodic Function Order Estimate Exact Order Exact Order Estimate Trigonometric Width 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    R. S. Ismagilov, “Widths of sets in linear normed spaces and approximation of functions by trigonometric polynomials,” Usp. Mat. Nauk, 29, No. 3, 161–178 (1974).Google Scholar
  2. 2.
    V. E. Maiorov, “On linear widths of Sobolev classes and chains of extremal spaces,” Mat. Sb., 113, No. 3, 437–463 (1980).Google Scholar
  3. 3.
    Y. Makovoz, “On trigonometric n-widths and their generalizations,” J. Approxim. Theory, 41, No. 4, 361–366 (1984).Google Scholar
  4. 4.
    É. S. Belinskii, “Approximation of periodic functions by a “floating” system of exponentials and trigonometric widths],” in: Investigations in the Theory of Functions of Many Real Variables [in Russian], Yaroslavl University, Yaroslavl (1984), pp. 10–24.Google Scholar
  5. 5.
    É. S. Belinskii, “Approximation of periodic functions of many variables by a “floating” system of exponentials and trigonometric widths,” Dokl. Akad. Nauk SSSR, 284, No. 6, 1294–1297 (1985).Google Scholar
  6. 6.
    V. N. Temlyakov, “Approximation of functions with bounded mixed derivative,” Tr. Mat. Inst. Akad. Nauk SSSR, 178 (1986).Google Scholar
  7. 7.
    A. S. Romanyuk, “Trigonometric widths of the classes B r p ??of functions of many variables in the space L q,” Ukr. Mat. Zh., 50, No. 8, 1089–1097 (1998).Google Scholar
  8. 8.
    Sun Yongsheng and Wang Heping, “Representation and approximation of multivariate periodic functions with bounded mixed moduli of smoothness,” Tr. Mat. Inst. RAN, 219, 356–377 (1997).Google Scholar
  9. 9.
    N. K. Bari and S. B. Stechkin, “Best approximations and differential properties of two conjugate functions,” Tr. Mosk. Mat. Obshch., 5, 483–522 (1956).Google Scholar
  10. 10.
    É. S. Belinskii and É. M. Galeev, “On the least value of norms of mixed derivatives of trigonometric polynomials with given number of harmonics,” Vestn. Mosk. Univ., Ser. Mat. Mekh., No. 2, 3–7 (1991).Google Scholar
  11. 11.
    S. M. Nikol'skii, Approximation of Periodic Functions of Many Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1977).Google Scholar
  12. 12.
    G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, Cambridge, (1934).Google Scholar
  13. 13.
    N. N. Pustovoitov, “Representation and approximation of periodic functions of many variables with given mixed modulus of continuity,” Anal. Math., 20, 35–48 (1994).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • S. A. Stasyuk
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

Personalised recommendations