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

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. [References: 24]