Inversion of many-dimensional Mellin transforms and

I. A. Antipova

Sbornik. Mathematics, Tome 198 (2007) no. 4, pp. 447-463

Résumé

For an arbitrary pair of convex domains $U,\Theta\subset\mathbb R^n$ one introduces mirror-symmetric vector spaces $M_\Theta^U$ and $W_U^\Theta$ consisting of holomorphic functions in the corresponding domains and taken to each other by the direct and the inverse Mellin transformations. As applications, a generalization of the classical integral Mellin transform for a solution $y(x)$ of the general algebraic equation is obtained and the convergence domain of the Mellin–Barnes hypergeometric integral representing the solution $y(x)$ is found. Bibliography: 10 titles.