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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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##### References:
 [1] Die Kontorovich-Lebedev-Transformation und die Mehler-Fock-Transformation verallgemeinerter Funktionen, Dissertation, TH Darmstadt 1977 [2] et al., Higher transcendental functions, vol. 1, McGraw-Hill, New York 1953 · Zbl 0051.30303 [3] Some investigations on the Mehler-Fock-transformation of distributions, Proc. Conf. ”Convergence and Generalized Functions”, Katowice 1983, Warszawa 1984 [4] Glaeske, Math. Nachr. [5] Russian Language Ignored 1973 [6] Russian Language Ignored 1981 [7] The use of integral transforms, McGraw-Hill, New York 1972 · Zbl 0237.44001 [8] Russian Language Ignored 118 pp 219– (1958) [9] Generalized integral transformations, Interscience, New York 1968
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