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A generalized Meijer transformation. (English) Zbl 0597.46036
Two generalized Meijer transformations introduced in [E. Krätzel, Proc. Conf., Generalized Functions and Operational Calculus, Varna 1975, 148-155 (1979; Zbl 0403.44003)] are extended to distributions. Two test function spaces are defined in which the respective kernels involved are elements. The distributional generalized Meijer transformation and the distributional Meijer-Laplace transformation are obtained by applying elements in the respective dual spaces to the appropriate kernel. Properties of these distributional transforms, such as analyticity, uniqueness, and inversion, are obtained.
Reviewer: R.D.Carmichael

MSC:
46F12 Integral transforms in distribution spaces
46F05 Topological linear spaces of test functions, distributions and ultradistributions
44A15 Special integral transforms (Legendre, Hilbert, etc.)
44A20 Integral transforms of special functions
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