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Mehler Integral Transforms Associated with Jacobi Functions with Respect to the Dual Variable

✍ Scribed by N. Ben Salem; K. Trimèche

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 355 KB
Volume: 214
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5623

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✦ Synopsis

We prove a Mehler representation for Jacobi functions t with respect to the dual variable . We exploit this representation to define a pair of dual integral transforms and its transposed t . We define two second order difference

. operators P and Q such that t is an eigenfunction of P with respect ␣, ␤ ␣ , ␤ to the dual variable , and and t are permutation operators between P ␣ , ␤ ␣ , ␤ ␣ , ␤ and Q. Next we give some spaces of functions on which and t are ␣ , ␤ ␣ , ␤

isomorphisms and we establish inversion formulas for these transforms.

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