Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-29T05:36:54.205Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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