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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Recovery of $ H\sp{p}$-functions


Author: V. Totik
Journal: Proc. Amer. Math. Soc. 90 (1984), 531-537
MSC: Primary 30D55
DOI: https://doi.org/10.1090/S0002-9939-1984-0733401-3
MathSciNet review: 733401
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Abstract: Let there be given finitely many points $ \{ {\alpha _k}\} _1^n$ from the unit disc. If $ f$ is a $ {H^p}$-function then how well can the value of $ f$ at $ z = 0$ be approximated by linear means $ \sum\nolimits_1^n {{c_k}f({\alpha _k})?} $ We give the optimal constants $ {c_k}$ and get, as a corollary, the possibility of the approximation of $ f$ by operators of the form $ \sum\nolimits_1^n {f({\alpha _k}){p_k}} $ with polynomials $ {p_k}$. The order of approximation depends on the distance $ \sum\nolimits_1^n {\left( {1 - \left\vert {{\alpha _k}} \right\vert} \right)} $ of the point system from the unit circle.


References [Enhancements On Off] (What's this?)

  • [1] Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962. MR 0133008
  • [2] Harold S. Shapiro, Topics in approximation theory, Springer-Verlag, Berlin-New York, 1971. With appendices by Jan Boman and Torbjörn Hedberg; Lecture Notes in Math., Vol. 187. MR 0437981
  • [3] G. Somorjai, On discrete linear operators in the function space $ A$, Proc. Constructive Function Theory (Blagoevgrad, 1977), Publ. H. Bulgarian Acad. Sci., Sofia, 1980, pp. 489-500.
  • [4] A. F. Timan, Theory of approximation of functions of a real variable, Hindustan, Delhi, 1966.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0733401-3
Keywords: $ {H^p}$ spaces, disc algebra, approximation
Article copyright: © Copyright 1984 American Mathematical Society