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The excess of sets of complex exponentials


Author: David R. Peterson
Journal: Proc. Amer. Math. Soc. 44 (1974), 321-325
MSC: Primary 42A64
DOI: https://doi.org/10.1090/S0002-9939-1974-0340946-0
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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  • [1] W. O. Alexander and R. Redheffer, The excess of sets of complex exponentials, Duke Math. J. 34 (1967), 59-72. MR 34 #6432. MR 0206614 (34:6432)
  • [2] A. Beurling and P. Malliavin, On the closure of characters and the zeros of entire functions, Acta Math. 118 (1967), 79-93. MR 35 #654. MR 0209758 (35:654)
  • [3] J. Elsner, Zulässige Abänderungen von Exponential-systemen im $ {L^p}( - A,A)$, Math. Z. 120 (1971), 211-220. MR 0435721 (55:8679)
  • [4] M. I. Kadec, The exact value of the Paley-Wiener constant, Dokl. Akad. Nauk SSSR 155 (1964), 1253-1254 = Soviet Math. Dokl. 5 (1964), 559-561. MR 28 #5289. MR 0162088 (28:5289)
  • [5] A. E. Ingham, Some trigonometrical inequalities with applications to the theory of series, Math. Z. 41 (1936), 367-379. MR 1545625
  • [6] J. Kahane, Travaux de Beurling et Malliavin, Séminaire Bourbaki, 1961/1962, fasc. 1, Exposé 225, 2ième éd., Secrétariat mathématique, Paris, 1962. MR 26 #3561; errata, 30, 1203.
  • [7] N. Levinson, Gap and density theorems, Amer. Math. Soc. Colloq. Publ., vol. 26, Amer. Math. Soc., Providence, R.I., 1940. MR 2, 180. MR 0003208 (2:180d)
  • [8] R. E. A. C. Paley and N. Wiener, Fourier transforms in the complex domain, Amer. Math. Soc. Colloq. Publ., vol. 19, Amer. Math. Soc., Providence, R.I., 1934. MR 1451142 (98a:01023)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0340946-0
Keywords: Completeness, excess
Article copyright: © Copyright 1974 American Mathematical Society

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