Skip to main content
SpringerLink
Log in

Inverse theorems for approximation by harmonic functions

  • 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. I. P. Natanson, “On the order of approximation of a continuous 2π-periodic function with the help of its Poisson integral,” Dokl. Akad. Nauk SSSR,72, No. 1, 11–14 (1950).

    Google Scholar 

  2. A. F. Timan, “Sharp estimate of the remainder in the approximation of differentiable periodic functions by the Poisson integrals,” Dokl. Akad. Nauk SSSR,74, No. 1, 17–20 (1950).

    Google Scholar 

  3. Ya. L. Geronimus, “On the order of approximation by means of the Poisson integral,” Dokl. Akad. Nauk SSSR,129, No. 4, 726–728 (1959).

    Google Scholar 

  4. M. F. Timan, “Deviation of harmonic functions from their values on the boundary and the best approximation,” Dokl. Akad. Nauk SSSR,145, No. 5, 1008–1009 (1962).

    Google Scholar 

  5. V. I. Gorbaichuk and P. V. Zaderei, “On certain boundary properties of harmonic functions in a strip,” Mat. Zametki,18, No. 2, 169–178 (1975).

    Google Scholar 

  6. V. I. Gorbaichuk and P. V. Zaderei, “Properties of solutions of the Dirichlet problem for a disk and a strip,” in: Mathematical Collection [in Russian], Naukova Dumka, Kiev (1976), pp. 64–68.

    Google Scholar 

  7. V. I. Gorbaichuk and M. V. Lukiyanchuk, “Boundary properties of solutions of the equation Δu-c2u=0 in the half plane,” Monogenic Functions and Mappings [in Russian], N. P. Korneichuk (ed.), Naukova Dumka, Kiev (1982), pp. 75–80.

    Google Scholar 

  8. V. I. Gorbaichuk and M. V. Lukiyanchuk, “A study of certain boundary properties of solutions of the equation Δu-c2u-0 in the half plane,” Ukr. Mat. Zh.,35, No. 6, 681–688 (1983).

    Google Scholar 

  9. A. F. Timan, Theory of Approximation of Functions of a Real Variable [in Russian], Gosudarstvennoe Izd. Fizikomatematicheskoi Literatury, Moscow (1960).

    Google Scholar 

  10. V. I. Gorbaichuk, “Direct and inverse theorem for approximation by solutions of boundaryvalue problems for certain elliptic equations,” in: Theory of Approximation of Functions [in Russian], S. B. Stechkin and S. A. Telyakovskii (eds.), Proceedings of the International Conference on Theory of Approximation of Functions, Kaluga, 24–28 July, 1975, Nauka, Moscow (1977), pp. 126–128.

    Google Scholar 

  11. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press (1966).

Download references

Author information

Authors and Affiliations

  1. Lutsk Pedagogic Institute, USSR

    V. I. Gorbaichuk

Authors
  1. V. I. Gorbaichuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 38, No. 3, pp. 309–314, May–June, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gorbaichuk, V.I. Inverse theorems for approximation by harmonic functions. Ukr Math J 38, 266–271 (1986). https://doi.org/10.1007/BF01056821

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01056821

Keywords

Search

Navigation