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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 2024 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
Proc. Amer. Math. Soc. 45 (1974), 311-312
DOI: https://doi.org/10.1090/S0002-9939-1974-0350291-5
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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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Bibliographic 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