Mehler integral transforms associated with Jacobi functions with respect to the dual variable

[摘要] We prove a Mehler representation for Jacobi functions phi(lambda)((alpha,beta))(t) with respect to the dual variable lambda. We exploit this representation to define a pair of dual integral transforms chi(alpha,beta) and its transposed (t) chi(alpha,beta). We define two second order difference operators P-alpha,P-beta and Q such that phi(lambda)((alpha,beta))(t) is an eigenfunction of P-alpha,P-beta with respect to the dual variable lambda, and chi(alpha,beta) and (t) chi(alpha,beta) are permutation operations between P-alpha,P-beta and Q. Next we give some spaces of functions on which chi(alpha,beta) and (t) chi(alpha,beta) are isomorphisms and we establish inversion formulas for these transforms. (C) 1997 Academic Press.

[发布日期] 1997-10-15