PLANCHEREL AND PALEY-WIENER THEOREMS FOR AN INDEX INTEGRAL TRANSFORM

  • Kim, Vu--Tuan (Department of Mathematics and Computer Science Faculty of Science, Kuwait University) ;
  • Ali Ismail (Department of Mathematics and Computer Science Faculty of Science, Kuwait University) ;
  • Megumi Saigo (Department of Applied Mathematics Fukuoka University)
  • Published : 2000.07.01

Abstract

An integral transform with the Bessel function Jv(z) in the kernel is considered. The transform is relatd to a singular Sturm-Liouville problem on a half line. This relation yields a Plancherel's theorem for the transform. A Paley-Wiener-type theorem for the transform is also derived.

Keywords

Plancherel therorem;Paley-Wiener theorem;singular Sturm-Liouville problem, index transform;Bessel function

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