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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 3, Pages 632–640
DOI: https://doi.org/10.17377/smzh.2017.58.312
(Mi smj2885)
 

This article is cited in 2 scientific papers (total in 2 papers)

A criterion for the convergence of the Mellin–Barnes integral for solutions to simultaneous algebraic equations

V. R. Kulikov

Siberian Federal University, Krasnoyarsk, Russia
Full-text PDF (291 kB) Citations (2)
References:
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.
Keywords: algebraic equations, Mellin–Barnes integral, hypergeometric functions, convergence domain.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.Y26.31.0006
НШ-9149.2016.1
This research was conducted at Siberian Federal University and supported by the Government of the Russian Federation (Grant 14.Y26.31.0006) and the State Maintenance Program for the Leading Scientific Schools (Grant NSh-9149.2016.1).
Received: 25.06.2016
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 3, Pages 493–499
DOI: https://doi.org/10.1134/S0037446617030120
Bibliographic databases:
Document Type: Article
UDC: 517.55
MSC: 35R30
Language: Russian
Citation: V. R. Kulikov, “A criterion for the convergence of the Mellin–Barnes integral for solutions to simultaneous algebraic equations”, Sibirsk. Mat. Zh., 58:3 (2017), 632–640; Siberian Math. J., 58:3 (2017), 493–499
Citation in format AMSBIB
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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