Paley-Wiener-type theorems for a class of integral transforms

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:266

Article

Tuan, VK ; Zayed, AI

关键词: Paley-Wiener theorem;    singular Sturm-Liouville problems;    Fourier transform;    Hankel transform;    Weber transform;    Jacobi transform;    Kontorovich-Lebedev transform;   

DOI  :  10.1006/jmaa.2001.7740

来源: Elsevier

【 摘 要 】

A characterization of weighted L-2(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. (C) 2002 Elsevier Science.

【 授权许可】

Free