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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
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?)

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Keywords: $ {H^p}$ spaces, disc algebra, approximation
Article copyright: © Copyright 1984 American Mathematical Society