A weighted version of the Paley–Wiener theorem
Published online by Cambridge University Press: 24 October 2008
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
References
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