Inversion of many-dimensional Mellin transforms and solutions of algebraic equations
Irina Avgustovna Antipova · Sbornik Mathematics · 2007
For an arbitrary pair of convex domains one introduces mirror-symmetric vector spaces and? 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 ?of the general algebraic equation is obtained and the convergence domain of?the Mellin-Barnes hypergeometric integral representing the solution is found.Bibliography: 10 titles.