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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
DOI: https://doi.org/10.1090/S0002-9939-1974-0350291-5
MathSciNet review: 0350291
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Abstract | References | Similar Articles | Additional Information

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?)

  • 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 <IMG WIDTH="33" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img4.gif" ALT="${H^2}$">
Article copyright: © Copyright 1974 American Mathematical Society