Skip to main content
Log in

Approximation properties of systems of exponentials in one space of analytic functions

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We obtain a criterion of completeness of a system of exponentials in the Hardy-Smirnov spaces in unbounded convex polygons and study the properties of incomplete systems of exponentials.

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.

Similar content being viewed by others

References

  1. B. V. Vinnitskii, “On zeros of functions analytic in a half plane and completeness of systems of exponents,” Ukr. Mat. Zh., 46, No. 5, 484–500 (1994).

    Article  MathSciNet  Google Scholar 

  2. M. M. Dzhrbashyan and V. M. Martirosyan, “Theorems of the Paley-Wiener and Miintz-Szasz types,” lzv. Akad. Nauk. SSSR, Ser Mat., 44, No. 1, 868–894 (1977).

    Google Scholar 

  3. A. O. Gel’fond, Calculus of Finite Differences [in Russian], Gostekhizdat, Moscow 1952.

    Google Scholar 

  4. N. V. Govorov, Riemann Boundary-Value Problem with Infinite Index [in Russian], Nauka, Moscow 1986.

    MATH  Google Scholar 

  5. B. V. Vinnitskii and A. V. Shapovalovskii, “On the completeness of systems of exponents with weight,” Ukr. Mat. Zh., 41, No 12, 1695–1700 (1989).

    Article  MathSciNet  Google Scholar 

  6. M. M. Dzhrbashyan, Integral Transformations and Representations of Functions in the Complex Domain [in Russian], Nauka, Moscow 1966.

    Google Scholar 

  7. A. M. Sedletskii, “Equivalent definition of H p spaces in a half plane and some applications,” Mat. Sb., 96 (138), No. 1, 75–82 (1975).

    MathSciNet  Google Scholar 

  8. A. F. Leont’ev, Entire Functions. Series of Exponentials [in Russian], Nauka, Moscow 1983.

    Google Scholar 

  9. B. Ya. Levin and Yu. I. Lyubarskii, “Interpolation by entire functions from special classes and related expansions into series of exponentials,” lzv. Akad. Nauk SSSR, Ser. Mat., 39, No. 3, 657–702 (1975).

    MATH  Google Scholar 

  10. J. B. Garnett, Bounded Analytic Functions [Russian translation], Mir, Moscow 1984.

    MATH  Google Scholar 

  11. R. Paley and N. Wiener, Fourier Transforms in the Complex Domain [Russian translation], Nauka, Moscow 1964.

    MATH  Google Scholar 

  12. B. Ya. Levin, Root Distribution of Entire Functions [in Russian], Gostekhizdat, Moscow 1956.

    Google Scholar 

  13. K. Hoffman, Banach Spaces of Analytic Functions [Russian translation], Inostrannaya Literatura, Moscow 1963.

    MATH  Google Scholar 

  14. A. F. Leont’ev, Sequences of Polynomials in Exponentials [in Russian], Nauka, Moscow 1980.

    Google Scholar 

  15. L. Schwartz, Etude des Sommes D’exponentiellees Reeles, Herman, Paris 1943.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vinnitskii, B.V. Approximation properties of systems of exponentials in one space of analytic functions. Ukr Math J 48, 189–206 (1996). https://doi.org/10.1007/BF02372045

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02372045

Keywords

Navigation