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On the convolution theorem of the Mehler-Fock-transform for a class of generalized functions. II. (English) Zbl 0649.46037
In part I the authors had obtained the result concerning the convolution structure of the Mehler-Fock-transform of order zero \[ {\mathcal F}(\tau)=\int^{\infty}_{1}f(t)P_{i\tau -{1/2}}(t)dt \] for certain space of generalized function [ibid. 131, 107-117 (1987; Zbl 0633.46038)]. In this paper, the authors extend the preceding result to the case of order \(n\geq 0\), \[ {\mathcal F}_ n(\tau)=\int^{\infty}_{1}f(t)P^{-n}_{i\tau -}(t)dt, \] where the kernel is a cone function of order n defined by \[ P^{-n}_{i\tau- {1/2}}(t)=\frac{1}{2^ n n!}(t^ 2-1)^{n/2}\cdot_ 2F_ 1(n+{1/2}+i\tau,n+{1/2}-i\tau:n+1;(1-t)/2). \]
Reviewer: Y.Tanno

MSC:
46F12 Integral transforms in distribution spaces
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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