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A weighted version of the Paley–Wiener theorem

Published online by Cambridge University Press:  24 October 2008

T. G. Genchev
T. G. Genchev
Affiliation:
Mathematics Faculty of Sofia University, A. Ivanov 5, 1126 Sofia, Bulgaria
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Extract

A generalization of the classical theorems of Paley and Wiener[5] and Plancherel and Polya[6] concerning entire functions of exponential type is obtained. The proof relies only on the Cauchy theorem and the Hardy–Littlewood inequality for the Fourier transform (see [8, 9]). Since the functions under consideration are supposed to be defined only in two opposite octants in ℂn, a version of the edge of the wedge theorem [7] is derived as a by-product.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 389 - 395
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

REFERENCES

[1]Boas, R. P.. Entire Functions (Academic Press, 1954).Google Scholar
[2]Genchev, T. G.. Entire functions of exponential type with polynomial growth on . J. Math. Anal. Appl. 60, no. 1(1977), 103–119.Google Scholar
[3]Hörmander, L.. Linear Partial Differential Operators (Springer-Verlag, 1963).Google Scholar
[4]Mikusinski, J. G.. On the Paley–Wiener Theorem. Studia Math. 13 (1953), 287–295.Google Scholar
[5]Paley, R. F. A. C. and Wiener, N.. Fourier Transforms in the Complex Domain (American Mathematical Society, 1934).Google Scholar
[6]Plancherel, M. and Polya, G.. Fonctions entières et intégrales de Fourier multiples. Comment. Math. Helv. 9 (1937), 224–248.Google Scholar
[7]Rudin, W.. Lectures on the Edge of the Wedge Theorem (American Mathematical Society, 1971).Google Scholar
[8]Sadosky, C.. Interpolations of Operators and Singular Integrals (Marcel Dekker, 1978).Google Scholar
[9]Titchmarsh, E. C.. Introduction to the Theory of Fourier Integrals (Clarendon Press, 1937).Google Scholar