Two consequences of the Beurling-Malliavin theory
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- by Ray Redheffer PDF
- Proc. Amer. Math. Soc. 36 (1972), 116-122 Request permission
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
- William O. Alexander Jr. and Ray Redheffer, The excess of sets of complex exponentials, Duke Math. J. 34 (1967), 59–72. MR 206614
- Arne Beurling and Paul Malliavin, On the closure of characters and the zeros of entire functions, Acta Math. 118 (1967), 79–93. MR 209758, DOI 10.1007/BF02392477 J.-P. Kahane, Travaux de Beurling et Malliavin, Séminaire Bourbaki 1961/62, Benjamin, New York, 1966, pp. 225-01, 225-213. MR 33 #5420i. R. M. Redheffer, Three problems in elementary analysis, Bull. Amer. Math. Soc. 72 (1966), 221-223.
- Raymond M. Redheffer, Elementary remarks on completeness, Duke Math. J. 35 (1968), 103–116. MR 225090 —, A note on completeness, Notices Amer. Math. Soc. 16 (1967), 830. Abstract #67T-583.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 116-122
- MSC: Primary 42A64
- DOI: https://doi.org/10.1090/S0002-9939-1972-0322439-8
- MathSciNet review: 0322439