Rao, G. L. N.; Debnath, L. A generalized Meijer transformation. (English) Zbl 0597.46036 Int. J. Math. Math. Sci. 8, 359-365 (1985). 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 Cited in 1 ReviewCited in 3 Documents 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 Keywords:distributional generalized Meijer transformation; distributional Meijer- Laplace transformation; analyticity; uniqueness; inversion Citations:Zbl 0403.44003 PDFBibTeX XMLCite \textit{G. L. N. Rao} and \textit{L. Debnath}, Int. J. Math. Math. Sci. 8, 359--365 (1985; Zbl 0597.46036) Full Text: DOI EuDML