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


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


Zbl 0403.44003
Full Text: DOI EuDML