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.
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).
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
\Bibitem{Kul17}
\by V.~R.~Kulikov
\paper A criterion for the convergence of the Mellin--Barnes integral for solutions to simultaneous algebraic equations
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 3
\pages 632--640
\mathnet{http://mi.mathnet.ru/smj2885}
\crossref{https://doi.org/10.17377/smzh.2017.58.312}
\elib{https://elibrary.ru/item.asp?id=29160454}
\transl
\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 3
\pages 493--499
\crossref{https://doi.org/10.1134/S0037446617030120}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000404212100012}
\elib{https://elibrary.ru/item.asp?id=31029899}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85021277201}
Linking options:
https://www.mathnet.ru/eng/smj2885
https://www.mathnet.ru/eng/smj/v58/i3/p632
This publication is cited in the following 2 articles:
Vladimir R. Kulikov, “Hypergeometric series and the Mellin–Barnes integrals for zeros of a system of Laurent polynomials”, Zhurn. SFU. Ser. Matem. i fiz., 13:1 (2020), 87–96
Irina A. Antipova, Ekaterina A. Kleshkova, Vladimir R. Kulikov, “Analytic continuation for solutions to the system of trinomial algebraic equations”, Zhurn. SFU. Ser. Matem. i fiz., 13:1 (2020), 114–130
Citation in format AMSBIB
Contact us: