A criterion for the convergence of the Mellin–Barnes integral for solutions to simultaneous algebraic equations
- Authors: Kulikov V.R.1
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Affiliations:
- Siberian Federal University
- Issue: Vol 58, No 3 (2017)
- Pages: 493-499
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171226
- DOI: https://doi.org/10.1134/S0037446617030120
- ID: 171226
Cite item
Abstract
We obtain a criterion for the convergence of the Mellin–Barnes integral representing the solution to a general system of algebraic equations. This yields a criterion for a nonnegative matrix to have positive principal minors. The proof rests on the Nilsson–Passare–Tsikh Theorem about the convergence domain of the general Mellin–Barnes integral, as well as some theorem of a linear algebra on a subdivision of the real space into polyhedral cones.
About the authors
V. R. Kulikov
Siberian Federal University
Author for correspondence.
Email: v.r.kulikov@mail.ru
Russian Federation, Krasnoyarsk