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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 ν 0 by E. Krätzel [see “Generalized functions and operational calculus, Proc. Conf., Varna, 1975, 148-155, Bulgar. Acad. Sci., Sofia (1979; Zbl 0403.44003); see also E. Krätzel and 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 (I). Several properties, namely, analyticity, boundedness and an inversion theorem are established for the generalized transformation on the dual space ' (I). As a particular case, another inversion formula for the Meijer transform is also derived.
MSC:
46F12Integral transforms in distribution spaces
44A15Special transforms (Legendre, Hilbert, etc.)