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On the excess of sets of complex exponentials

Authors: Nobuhiko Fujii, Akihiro Nakamura and Ray Redheffer
Journal: Proc. Amer. Math. Soc. 127 (1999), 1815-1818
MSC (1991): Primary 30B60
Published electronically: February 17, 1999
MathSciNet review: 1476126
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Abstract: For $-\infty<n<\infty$ let $\mu _n$ be complex numbers such that $\mu _n-n$ is bounded. For $n>0$ define $\lambda _n=\mu _n+a$, $\lambda _{-n}=\mu _{-n}-b$ where $a,b\ge 0$. Then the excesses $E$ in the sense of Paley and Wiener satisfy $E(\{\lambda _n\})\le E(\{\mu _n\})$.

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

  • [1] Levinson, Norman, Gap and Density Theorems, AMS Colloquium Publication XXVI (1940), Chapters I, III and IV. MR 2:180d
  • [2] Paley, Raymond E. A. C and Norbert Wiener, Fourier Transforms in the Complex Domain, AMS Colloquium Publication XIX (1934), Chapter VI. CMP 97:13
  • [3] Redheffer, Raymond M., Completeness of Sets of Complex Exponentials, Advances in Mathematics 24 (1977) 1-62. MR 56:5852
  • [4] Schwartz, Laurent, Approximation d'une fonction quelconque par des sommes d'exponentielles imaginaires, Ann. Fac. Sci. Toulouse (1943), 111-176. Reprint (Paris 1959) with some additions.
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Additional Information

Nobuhiko Fujii
Affiliation: Department of Mathematics, Tokai University, 3-20-1 Orido, Shimizu, Shizuoka 424-8610, Japan

Akihiro Nakamura
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555

Received by editor(s): January 31, 1997
Received by editor(s) in revised form: September 20, 1997
Published electronically: February 17, 1999
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1999 American Mathematical Society

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