Inversion of many-dimensional Mellin transforms and solutions of algebraic equations

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.