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Two consequences of the Beurling-Malliavin theory

Author: Ray Redheffer
Journal: Proc. Amer. Math. Soc. 36 (1972), 116-122
MSC: Primary 42A64
MathSciNet review: 0322439
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Abstract: If $ (1/{\lambda _n}) - (1/{\mu _n})$ forms an absolutely convergent series, then $ \{ \exp (i{\lambda _n}x)\} $ and $ \{ \exp (i{\mu _n}x)\} $ have the same completeness interval. This follows from a new formula for the completeness radius which is simpler than the well-known formula of Beurling and Malliavin.

References [Enhancements On Off] (What's this?)

  • [1] William O. Alexander Jr. and Ray Redheffer, The excess of sets of complex exponentials, Duke Math. J. 34 (1967), 59–72. MR 0206614
  • [2] Arne Beurling and Paul Malliavin, On the closure of characters and the zeros of entire functions, Acta Math. 118 (1967), 79–93. MR 0209758
  • [3] J.-P. Kahane, Travaux de Beurling et Malliavin, Séminaire Bourbaki 1961/62, Benjamin, New York, 1966, pp. 225-01, 225-213. MR 33 #5420i.
  • [4] R. M. Redheffer, Three problems in elementary analysis, Bull. Amer. Math. Soc. 72 (1966), 221-223.
  • [5] Raymond M. Redheffer, Elementary remarks on completeness, Duke Math. J. 35 (1968), 103–116. MR 0225090
  • [6] -, A note on completeness, Notices Amer. Math. Soc. 16 (1967), 830. Abstract #67T-583.

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Article copyright: © Copyright 1972 American Mathematical Society