Paley-Wiener-Type Theorems For A Class Of Integral Transforms
Fourier transform; Hankel transform; Jacobi transfom; Kontorovich-Lebedev transform; Paley-Wiener theorem; Singular Sturm-Liouville problems; Weber transform
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. ©c 2002 Elsevier Science.
Journal of Mathematical Analysis and Applications
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Tuan, Vu Kim and Zayed, Ahmed I., "Paley-Wiener-Type Theorems For A Class Of Integral Transforms" (2002). Scopus Export 2000s. 2642.