Skip to main content
SpringerLink
Log in

On a constructive characterization of functions from the classes DrHω2(t) on closed sets with a piecewise smooth boundary

  • Published:
Ukrainian Mathematical Journal Aims and scope

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

Literature cited

  1. V. K. Dzyadyk, “On a problem of S. M. Nikol'skii in a complex domain,” Izv. Akad. Nauk SSSR, Ser. Matem.,23, No. 4 (1959).

  2. V. K. Dzyadyk, “On the problem of approximating continuous functions in closed domains with corners, and a problem of S. M. Nikol'skii (first communication),” Izv. Akad. Nauk SSSR, Ser. Matem.,26, No. 6 (1962).

  3. V. K. Dzyadyk, “On the theory of approximation of analytic functions, which are continuous in closed domains, and a problem of S. M. Nikol'skii (second communication),” Izv. Akad. Nauk SSSR, Ser. Matem.,27, No. 5 (1963).

  4. V. K. Dzyadyk, “Inverse theorems in the theory of approximation of functions in complex domains,” Ukrainsk. Matem. Zh.,15, No. 4, 365–375 (1963).

    Google Scholar 

  5. V. K. Dzyadyk, “On analytic and harmonic transformations and the approximation of harmonic functions,” Ukrainsk. Matem. Zh.,19, No. 5 (1967).

  6. V. K. Dzyadyk and O. I. Shvai, “A constructive characterization of functions of Holder classes in regions with piecewise smooth boundary and arbitrary positive exterior angles,” Dopovidi Akad. Nauk UkrRSR, Ser. A, No. 11, 1012–1015 (1967).

    Google Scholar 

  7. V. K. Dzyadyk and G. A. Alibekov, “On the unfirom approximation of functions of a complex variable on closed domains with corners,” Matem. Sb.,75, No. 4 (1968).

  8. V. K. Dzyadyk, “On the constructive characterization of functions of the Hölder classes on closed sets with a piecewise smooth boundary, which admits zero angles,” Ukrainsk. Matem. Zh.,20, No. 5 (1968).

  9. N. A. Lebedev and P. M. Tamrazov, “Inverse theorems for the approximation on regular compact sets of the complex plane,” Izv. Akad. Nauk SSSR, Ser. Matem.,34, No. 6 (1970).

  10. N. A. Lebedev and N. A. Shirokov, “On the uniform approximation of functions on closed sets, which have a finite number of corners with nonzero exterior angles,” Izv. Akad. Nauk ArmSSR,6, No. 4 (1971).

  11. V. K. Dzyadyk, “On an application of generalized Faber polynomials to the approximation of Cauchy type integrals and of functions of the classes Ar in domains with a smooth and piecewise smooth boundary,” Ukrainsk. Matem. Zh.,24, No. 1 (1972).

  12. R. V. Polyakov, “The approximation of functions continuous in domains with a smooth boundary (and analytic in the interior),” Ukrainsk. Matem. Zh.,24, No. 1 (1972).

  13. V. K. Dzyadyk and D. M. Galan, “On the approximation of analytic functions in domains with a smooth boundary,” Ukrainsk. Matem. Zh.,17, No. 1 (1965).

  14. V. V. Ivanov, “Some properties of singular integrals,” Izv. Vyssh. Ucheb. Zaved. Matematika, No. 4 (1948).

  15. V. I. Belyi, “On the approximation of quasismooth functions of a complex variable,” Izv. Akad. Nauk ArmSSR, Ser. Matem.,4, No. 5 (1969).

  16. V. K. Dzyadyk and I. A. Shevchuk, “On the limiting values of a Cauchy type integral for functions of the Zygmund classes,” Ukrainsk. Matem. Zh.,24, No. 5 (1972).

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, USSR

    I. A. Shevchuk

Authors
  1. I. A. Shevchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 25, No. 1, pp. 81–90, January–February, 1973.

I wish to express my deep gratitude to Dzyadyk for posing this problem, for some valuable observations, and for his constant interest in this work.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shevchuk, I.A. On a constructive characterization of functions from the classes DrHω2(t) on closed sets with a piecewise smooth boundary. Ukr Math J 25, 66–73 (1973). https://doi.org/10.1007/BF01085394

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01085394

Keywords

Search

Navigation