Paley–Wiener-Type Theorems for a Class of Integral Transforms

Authors: Tuan V.K.¹; Zayed A.I.²

Source: Journal of Mathematical Analysis and Applications, Volume 266, Number 1, February 2002 , pp. 200-226(27)

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Abstract:

A characterization of weighted L₂(I) spaces in terms of their images under various integral transformations is derived, where I is an interval (finite or infinite). This characterization is then used to derive Paley–Wiener-type theorems for these spaces. Unlike the classical Paley–Wiener theorem, our theorems use real variable techniques and do not require analytic continuation to the complex plane. The class of integral transformations considered is related to singular Sturm–Liouville boundary-value problems on a half line and on the whole line. © 2002 Elsevier Science.

Keywords: Paley–; Wiener theorem; singular Sturm–; Liouville problems; Fourier transform; Hankel transform; Weber transform; Jacobi transform; Kontorovich–; Lebedev transform

Language: English

Document Type: Research article

Affiliations: 1: Faculty of Science, Kuwait University, Safat, 13060, Kuwait 2: Department of Mathematics, University of Central Florida, Orlando, Florida, 32816

Publication date: 2002-02-01