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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

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