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Mathematical Notes

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

The problem of continuation with least coanalytic deviation

  • Yu. A. Dubinskii
Article

Abstract

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 

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References

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    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
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    N. K. Bari,Trigonometric Series [in Russian], Nauka, Moscow (1961).Google Scholar
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    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
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    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

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