Recovery of -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 from the unit disc. If is a -function then how well can the value of at be approximated by linear means We give the optimal constants and get, as a corollary, the possibility of the approximation of by operators of the form with polynomials . The order of approximation depends on the distance of the point system from the unit circle.

**[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*, 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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DOI:
https://doi.org/10.1090/S0002-9939-1984-0733401-3

Keywords:
spaces,
disc algebra,
approximation

Article copyright:
© Copyright 1984
American Mathematical Society