Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Recovery of $H^{p}$-functions
HTML articles powered by AMS MathViewer

by V. Totik PDF
Proc. Amer. Math. Soc. 90 (1984), 531-537 Request permission


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 $\sum \nolimits _1^n {\left ( {1 - \left | {{\alpha _k}} \right |} \right )}$ of the point system from the unit circle.
  • Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
  • Harold S. Shapiro, Topics in approximation theory, Lecture Notes in Mathematics, Vol. 187, Springer-Verlag, Berlin-New York, 1971. With appendices by Jan Boman and Torbjörn Hedberg. MR 0437981, DOI 10.1007/BFb0058976
  • 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. A. F. Timan, Theory of approximation of functions of a real variable, Hindustan, Delhi, 1966.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30D55
  • Retrieve articles in all journals with MSC: 30D55
Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 531-537
  • MSC: Primary 30D55
  • DOI:
  • MathSciNet review: 733401