Mathematical Notes

, Volume 64, Issue 1, pp 38–48 | Cite as

The problem of continuation with least coanalytic deviation

  • Yu. A. Dubinskii


The problem of continuing a function from the unit circle to the unit disk so that the continuation has the least deviation from the Sobolev subspace of analytic functions is considered. A mathematical model of this problem is constructed. It is proved that the problem is well-posed.

Key words

continuation of functions in the complex plane analytic function Sobolev space harmonic continuation complex Fourier series coanalytic deviation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Sh. Axler, “Bergman spaces and their applications,” in:Surveys of Some Recent Results in Operator Theory (Conway J., Morell B., editors), Vol. 1, Pitman Res. Notes Math. Ser., Longman Sci. Tech., Harlow (1988), pp. 1–50.Google Scholar
  2. 2.
    N. K. Bari,Trigonometric Series [in Russian], Nauka, Moscow (1961).Google Scholar
  3. 3.
    S. V. Shvedenko, “Hardy Classes and Related Spaces of Analytic Functions” [in Russian], Vol. 23, Itogi Nauki i Tekhniki. Mat. Anal., VINITI, Moscow (1985), pp. 3–124.Google Scholar
  4. 4.
    A. Zygmund,Trigonometric Series, Vol. 2, Cambridge: Cambridge Univ. Press (1960).Google Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • Yu. A. Dubinskii
    • 1
  1. 1.Moscow Power Engineering InstituteUSSR

Personalised recommendations