A generalized Meijer transformation (Q1079153)

Two generalized Meijer transformations introduced in [\textit{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.