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New inversion formulas for the Krätzel transformation. (English) Zbl 0989.46026
A generalization of the well-known Meijer transform introduced and denoted by $K^0_\nu$ by {\it E. Krätzel} [see “Generalized functions and operational calculus, Proc. Conf., Varna, 1975, 148-155, Bulgar. Acad. Sci., Sofia (1979; Zbl 0403.44003); see also {\it E. Krätzel} and {\it H. Menzer}, Publ. Math. Debrecen 18 (1971), 139-147 (1972; Zbl 0247.33014)] is analyzed by the authors applying the kernel method on the Schwartz space of distributions ${\cal E}(I)$. Several properties, namely, analyticity, boundedness and an inversion theorem are established for the generalized transformation on the dual space ${\cal E}'(I)$. As a particular case, another inversion formula for the Meijer transform is also derived.

46F12Integral transforms in distribution spaces
44A15Special transforms (Legendre, Hilbert, etc.)
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