The excess of sets of complex exponentials

Peterson, David R.

doi:10.1090/S0002-9939-1974-0340946-0

The excess of sets of complex exponentials
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by David R. Peterson PDF

Proc. Amer. Math. Soc. 44 (1974), 321-325 Request permission

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 $\sum {|{\lambda _n} - {\mu _n}|} < \infty$ 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.

References

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Travaux de Beurling et Malliavin

26

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