Skip to main content
Log in

Convergence and summability of fourier expansions in orthonormal polynomials associated with difference operators of second order

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. B. P. Osilenker, “Linear summability methods for Fourier expansions with respect to orthonormal polynomials,” Dokl. Akad. Nauk SSSR,209, No. 1, pp. 40–42 (1973).

    Google Scholar 

  2. Yu. M. Berezanskii, Expansions in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).

    Google Scholar 

  3. F. V. Atkinson, Discrete and Continous Boundary Problems [Russian translation], Mir, Moscow (1968); first published by Academic Press, New York (1964).

    Google Scholar 

  4. N. I. Akhiezer, “Infinite Jacobi matrices and the problem of moments,” Uspekhi Mat. Nauk,9, 126–156 (1941).

    Google Scholar 

  5. G. Aleksich, Convergence Problems for Orthogonal Series [Russian translation], IL, Moscow (1963).

    Google Scholar 

  6. G. Szego, Orthogonal Polynomials [Russian translation], GIFML, Moscow (1962).

    Google Scholar 

  7. B. P. Osilenker, “Summability of polynomial Fourier expansions of functions from the classes L Pμ(x) (p≥1),” Dokl. Akad. Nauk SSSR,202, No. 3, 529–531 (1972).

    Google Scholar 

  8. K. Tandori, “Über die Cesaroche Summierbarkeit der Orthogonalen Polynomreihen, II,” Acta Math. Acad. Sci. Hung.,V, No. 3-4, 237–252 (1954).

    Google Scholar 

  9. A. Zygmund, “The approximation of functions by typical means of their Fourier series,” Duke Math. J.,12, 695–704 (1945).

    Google Scholar 

  10. G. I. Natanson, “Summability of series in Jacobi polynomials by a method analogous to the method of Bernshtein-Rogozinskii,” Dokl. Akad. Nauk SSSR,92, No. 2, 229–230 (1953).

    Google Scholar 

  11. N. K. Bari, Trigometric Series [in Russian], GIFML, Moscow (1961).

    Google Scholar 

  12. A. Zygmund, Trigometric Series [Russian translation], Vol. I, Mir, Moscow (1965).

    Google Scholar 

  13. N. N. Lebedev, Special Functions and Their Applications [in Russian], GITTL, Moscow (1953).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 15, No. 4, pp. 892–908, July–August, 1974.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Osilenker, B.P. Convergence and summability of fourier expansions in orthonormal polynomials associated with difference operators of second order. Sib Math J 15, 632–643 (1974). https://doi.org/10.1007/BF00967439

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00967439

Keywords

Navigation