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This article is cited in 19 scientific papers (total in 19 papers)
Inversion of many-dimensional Mellin transforms and
solutions of algebraic equations
I. A. Antipova
Krasnoyarsk State Technical University
Abstract:
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.
DOI:
https://doi.org/10.4213/sm1562
 Full text:
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English version:
Sbornik: Mathematics, 2007, 198:4, 447–463
Bibliographic databases:
    
UDC:
517.55
MSC: Primary 44A30; Secondary 32A26
Received: 05.05.2006 and 07.12.2006
Citation:
I. A. Antipova, “Inversion of many-dimensional Mellin transforms and
solutions of algebraic equations”, Mat. Sb., 198:4 (2007), 3–20; Sb. Math., 198:4 (2007), 447–463
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Linking options:
http://mi.mathnet.ru/eng/msb1562https://doi.org/10.4213/sm1562 http://mi.mathnet.ru/eng/msb/v198/i4/p3
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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Mkrtchyan A.J., “Continuation of Multiple Power Series in a Sectorial Domain”, Math. Nachr.
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Irina A. Antipova, Tatyana V. Zykova, “O mnozhestve skhodimosti integrala Mellina–Barnsa, predstavlyayuschego resheniya tetranomialnogo algebraicheskogo uravneniya”, Zhurn. SFU. Ser. Matem. i fiz., 3:4 (2010), 475–486
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Zykova T.V., “O skhodimosti integrala Mellina–Barnsa na granitse ego oblasti skhodimosti”, Vestn. Kemerovskogo gos. un-ta, 2011, no. 3/1, 199–202
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I. A. Antipova, A. K. Tsikh, “The discriminant locus of a system of $n$ Laurent polynomials in $n$ variables”, Izv. Math., 76:5 (2012), 881–906
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I. A. Antipova, E. N. Mikhalkin, “Analytic continuations of a general algebraic function by means of Puiseux series”, Proc. Steklov Inst. Math., 279 (2012), 3–13
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Nilsson L., Passare M., “Mellin transforms of multivariate rational functions”, J. Geom. Anal., 23:1 (2013), 24–46
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Irina A. Antipova, Tatyana V. Zykova, “Mellin transform for monomial functions of the solution to the general polynomial system”, Zhurn. SFU. Ser. Matem. i fiz., 6:2 (2013), 150–156
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V. R. Kulikov, V. A. Stepanenko, “On solutions and Waring's formulae for the system of $n$ algebraic equations with $n$ unknowns”, St. Petersburg Math. J., 26:5 (2015), 839–848
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E. N. Mikhalkin, A. K. Tsikh, “Singular strata of cuspidal type for the classical discriminant”, Sb. Math., 206:2 (2015), 282–310
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E. N. Mikhalkin, “The monodromy of a general algebraic function”, Siberian Math. J., 56:2 (2015), 330–338
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Mkrtchyan A.J., “On Analytic Continuation of Multiple Power Series Beyond the Domain of Convergence”, J. Contemp. Math. Anal.-Armen. Aca., 50:1 (2015), 22–31
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I.A. Antipova, T.V. Zykova, “Mellin transforms and algebraic functions”, Integral Transforms and Special Functions, 2015, 1
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Beukers F., “Monodromy of A-hypergeometric functions”, J. Reine Angew. Math., 718 (2016), 183–206
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Artem V. Senashov, “On convergence of Mellin–Barnes integrals representing solutions of general algebraic systems of $3$ equations with $3$ variables”, Zhurn. SFU. Ser. Matem. i fiz., 10:3 (2017), 339–344
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I. A. Antipova, “On the Structure of the Bochner–Martinelli Residue Currents”, Proc. Steklov Inst. Math., 298 (2017), 1–12
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V. R. Kulikov, “A criterion for the convergence of the Mellin–Barnes integral for solutions to simultaneous algebraic equations”, Siberian Math. J., 58:3 (2017), 493–499
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Lisa Nilsson, Mikael Passare, August K. Tsikh, “Domains of convergence for $A$-hypergeometric series and integrals”, Zhurn. SFU. Ser. Matem. i fiz., 12:4 (2019), 509–529
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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
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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
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