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On the excess of sets of complex exponentials
Author(s):
Nobuhiko
Fujii;
Akihiro
Nakamura;
Ray
Redheffer
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1815-1818.
MSC (1991):
Primary 30B60
Posted:
February 17, 1999
MathSciNet review:
1476126
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Abstract:
For let be complex numbers such that is bounded. For define , where . Then the excesses in the sense of Paley and Wiener satisfy .
References:
- [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.
- [5]
- Young, Robert M., An Introduction to Nonharmonic Fourier Series, Academic Press 1980, Chapter 3. MR 81m:42027
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Additional Information:
Nobuhiko
Fujii
Affiliation:
Department of Mathematics, Tokai University, 3-20-1 Orido, Shimizu, Shizuoka 424-8610, Japan
Email:
nfujii@scc.u-tokai.ac.jp
Akihiro
Nakamura
Affiliation:
Department of Mathematics, Tokai University, 3-20-1 Orido, Shimizu, Shizuoka 424-8610, Japan
Ray
Redheffer
Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90095-1555
DOI:
10.1090/S0002-9939-99-04664-X
PII:
S 0002-9939(99)04664-X
Received by editor(s):
January 31, 1997
Received by editor(s) in revised form:
September 20, 1997
Posted:
February 17, 1999
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1999,
American Mathematical Society
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