Proceedings of the American Mathematical Society

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



Another proof of Szegő's theorem for a singular measure

Author: Finbarr Holland
Journal: Proc. Amer. Math. Soc. 45 (1974), 311-312
MSC: Primary 42A08; Secondary 30A78, 60G25
MathSciNet review: 0350291
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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 [Enhancements On Off] (What's this?)

  • [1] 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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Keywords: Singular probability measure, closed linear span, inner function, Hardy space $ {H^2}$
Article copyright: © Copyright 1974 American Mathematical Society