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


The excess of sets of complex exponentials

Author: David R. Peterson
Journal: Proc. Amer. Math. Soc. 44 (1974), 321-325
MSC: Primary 42A64
MathSciNet review: 0340946
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Abstract: Let $ \Lambda = \{ {\lambda _n}\} $ be a complex sequence and denote its associated set of complex exponentials $ \{ \exp (i{\lambda _n}x)\} $ by $ e(\Lambda )$. Redheffer and Alexander have shown that if $ \sum {\vert{\lambda _n} - {\mu _n}\vert} < \infty $ then $ e(\Lambda )$ and $ e(\mu )$ have the same excess over their common completeness interval. This paper shows this result to be the best possible.

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Additional Information

PII: S 0002-9939(1974)0340946-0
Keywords: Completeness, excess
Article copyright: © Copyright 1974 American Mathematical Society