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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

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Another proof of Szegő’s theorem for a singular measure
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by Finbarr Holland PDF
Proc. Amer. Math. Soc. 45 (1974), 311-312 Request permission

Abstract:

It is shown that the set $\{ {e^{\operatorname {int} }}:n \geqslant 1\}$ spans ${\mathfrak {L}^2}(\sigma )$ if $\sigma$ is a singular measure on the unit circle. The proof makes no appeal either to the F. and M. Riesz theorem on measures or to Hilbert space methods.
References
  • Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 45 (1974), 311-312
  • MSC: Primary 42A08; Secondary 30A78, 60G25
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0350291-5
  • MathSciNet review: 0350291