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Synopsisusing results of BUGGLE and TIWARI, PANDEY on the AlEHLER-FOCK-transforin in certain spaces of generalizcd functions we introduce a convolution structure for these spaces, such that a convolution theorem of the ~IEHLER-FocH-transform can he proved.

SynopsisWe extend in this paper the r a d t s of part (I) concerning the convolution structure of the ~-F o c~-t r~o r m of order zero to the case of ~m-FocK-transform of order n 2 0. This transform applies to generalized functions from spaces introduced by Bwaou. With these fe8ulf9 the operational calculus of this transform is completed.The M&mmn-Foc%s-transform of natural order n applied to ordinary functions obeying certain restrictions of their behaviour when the argumenk lands towards 1 or ca is defined by 00(1.1)where the kernel is a cone function of order n defined by 1 2^ n! := -(t2 -1)nln nP1(n + 112 + i z n + 1/.2it; ?z + 1;with the Gaussian hypergeometric function 3,. The operational properties of this tramformaiiion are represented in [7] chapter 7. There given applications to the solution of bonndq d u e problems too. In [lf Boaem investigated in hi5 thesis the IVIZHLg~-Boag-lxamForm of generaked functions and its applications. As well in the classical case of ordinary functions as in the caae of generalized functions a convolution theorem seems to be desirable. (Concerning a convolution in &-spaces see the references quoted in [a].) After the investigatbn of the convolution structure connected with the JS~HLEB-Fm-transform of order zero in part (I), (41, we present in *his paper similar results for the general ~-F~-t r a m f o m of order 11 already ske-without prooh in [3]. In view of the detailed exposition in the former paper we intend to expose only

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