Skip to main content
SpringerLink
Log in

Some properties of polynomials orthogonal in a space with “intermediate” topology. Kernel function and extremal properties

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

A space of holomorphic functions is considered. A topology in this space is “intermediate” between the topology of uniform convergence and the topology of uniform convergence on compact sets. The properties of systems of orthonormal polynomials are studied in Hilbert spaces with this topology.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Gaier,Vorlesungen über Approximation im Komplexen, Birkhäuser, Basel (1980).

    Google Scholar 

  2. V. I. Smirnov and N. A. Lebedev,Constructive Theory of Functions of Complex Variable [in Russian], Nauka, Moscow (1964).

    Google Scholar 

  3. A. A. Dovgoshei, “Approximation of analytic functions in certain functional spaces and rational approximation of functions belonging to the Hardy classes,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 10, 19–21 (1990).

    Google Scholar 

  4. A. A. Dovgoshei, “On the integral representations in the Hardy classes and the best approximations in certain functional spaces,”Ukr. Mat. Zh.,43, No. 3, 342–347 (1991).

    Google Scholar 

  5. P. K. Suétin,Classical Orthogonal Polynomials [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  6. P. L. Duren,Theory of H p-spaces, Academic Press, New York-London (1970).

    Google Scholar 

  7. A. A. Dovgoshei, “On the polynomial approximation for the functions from the Hardy classes in simply connected domains on a plane,”Ukr. Mat. Zh.,42, No. 9, 1266–1271 (1990).

    Google Scholar 

  8. G. M. Goluzin,Geometric Theory of Functions of Complex Variable [in Russian], Nauka, Moscow (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    A. A. Dovgoshei

Authors
  1. A. A. Dovgoshei
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 915–923, July, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dovgoshei, A.A. Some properties of polynomials orthogonal in a space with “intermediate” topology. Kernel function and extremal properties. Ukr Math J 45, 1012–1022 (1993). https://doi.org/10.1007/BF01057448

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01057448

Keywords

Search

Navigation