Skip to main content
SpringerLink
Log in

Reconstruction of linear functionals on classes of analytic functions of two variables on the basis of generalized information

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

For classes of analytic functions defined in terms of the two-dimensional Hadamard composition, we propose a renewal method for linear functionals based on blending constructions. The best renewal methods are indicated, and the exact estimates of errors are given.

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. S. A. Smolyak,On Optimal Reconstruction of Functions and Their Functional [in Russian], Dissertation, Candidate of Science (Physics and Mathematics), Moscow (1965).

    Google Scholar 

  2. N. S. Bakhvalov, “On the optimality of linear methods for approximating operators on convex classes of functions,”Zh. Vychisl. Mat. Mat. Fiz.,11, No. 1, 1014–1018 (1977).

    Google Scholar 

  3. B. D. Boyanov, “The best interpolation methods for some classes of differentiable functions,”Mat. Zametki,17, No. 4, 511–524 (1975).

    Google Scholar 

  4. B. D. Boyanov, “The best renewal of differentiable periodic functions by their Fourier coefficients,”Serdika. Bulg. Mat. Spisaniye,2, No. 4, 300–304 (1976).

    Google Scholar 

  5. V. L. Velikin, “Optimal interpolation of periodic differentiable functions with the bounded higher-order derivative,”Mat. Zametki,22, No. 5, 663–670 (1977).

    Google Scholar 

  6. A. A. Ligun, “Optimal methods for the approximate calculation of the functional of classesW'L ∞,”Anal. Math.,5, No. 4, 269–286 (1979).

    Google Scholar 

  7. K. Yu. Osipenko, “The best approximation of analytic functions on the basis of the information concerning their values at finitely many points,”Mat. Zametki,19, No. 1, 29–40 (1976).

    Google Scholar 

  8. M. P. Ovchintsev, “To the problem of optimal renewal of the functions of classE p in a ring,”Sib. Mat. Zh.,30, No. 4, 87–101 (1989).

    Google Scholar 

  9. V. N. Temlyakov, “On approximate renewal of periodic functions of several variables,”Dokl. Akad. Nauk SSSR,280, No. 6, 1310–1313 (1985).

    Google Scholar 

  10. M. Levin, “On the evaluation of double integrals,” in:Constructive Theory of Functions. Proceedings of the International Conference, Varna, June 1–5, 1981, Sofia (1983), pp. 414–418.

  11. M. Sh. Shabozov, “To the problem of reconstructing linear functionals on the basis of the information given in the form of boundary conditions,”Izv. Akad. Nauk Tadjik SSR, Ser. Fiz.-Mat., Khim. Geol. Nauk, 9–15 (1982).

  12. S. B. Vakarchuk, “On renewal of linear functionals, defined on classes of differentiable functions of two variables, on the basis of a generalized information,”Izv. Vysh. Uchebn. Zaved., Matematika, No. 2, 11–17 (1989).

    Google Scholar 

  13. A. K. Tsikh,Multidimensional Residues and Their Application [in Russian], Nauka, Novosibirsk (1988).

    Google Scholar 

  14. S. G. Samko, A. A. Kilbas and, O. N. Marichev,Integrals and Derivatives of Fractional Order and Their Applications [in Russian], Nauka i Tekhnika, Minsk (1987).

    Google Scholar 

  15. V. N. Belyi and M. Z. Dveirin, “On the best linear methods of approximation on classes of functions defined by adjoint kernels,”Metrich. Voprosy Teor. Funk. Otobrazhenyya, Issue 2, 37–54 (1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Geotechnical Mechanics, Ukrainian Academy of Sciences, Dnepropetrovsk

    S. B. Vakarchuk

Authors
  1. S. B. Vakarchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 32–37, January, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vakarchuk, S.B. Reconstruction of linear functionals on classes of analytic functions of two variables on the basis of generalized information. Ukr Math J 45, 33–39 (1993). https://doi.org/10.1007/BF01062035

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01062035

Keywords

Search

Navigation