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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A generalization of the Salem test


Author: Daniel Waterman
Journal: Proc. Amer. Math. Soc. 105 (1989), 129-133
MSC: Primary 42A20; Secondary 42A16
MathSciNet review: 929413
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Abstract: The Salem test is a criterion for uniform convergence of a Fourier series on the circle group. An improved test for convergence at a point and uniform convergence on an arbitrary set is obtained, as well as a necessary and sufficient condition for the convergence of the Fourier series of a function at a Lebesgue point.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0929413-1
PII: S 0002-9939(1989)0929413-1
Article copyright: © Copyright 1989 American Mathematical Society