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Mat. Sb., 2007, Volume 198, Number 4, Pages 3–20 (Mi msb1562)  

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.


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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

Citation in format AMSBIB
\by I.~A.~Antipova
\paper Inversion of many-dimensional Mellin transforms and
solutions of algebraic equations
\jour Mat. Sb.
\yr 2007
\vol 198
\issue 4
\pages 3--20
\jour Sb. Math.
\yr 2007
\vol 198
\issue 4
\pages 447--463

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    This publication is cited in the following articles:
    1. Mkrtchyan A.J., “Continuation of Multiple Power Series in a Sectorial Domain”, Math. Nachr.  crossref  mathscinet  isi
    2. 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  mathnet  elib
    3. Zykova T.V., “O skhodimosti integrala Mellina–Barnsa na granitse ego oblasti skhodimosti”, Vestn. Kemerovskogo gos. un-ta, 2011, no. 3/1, 199–202  mathscinet  elib
    4. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. 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  mathnet  crossref  mathscinet  isi  elib  elib
    6. Nilsson L., Passare M., “Mellin transforms of multivariate rational functions”, J. Geom. Anal., 23:1 (2013), 24–46  crossref  mathscinet  zmath  isi  elib  scopus
    7. 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  mathnet
    8. 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  mathnet  crossref  mathscinet  isi  elib  elib
    9. E. N. Mikhalkin, A. K. Tsikh, “Singular strata of cuspidal type for the classical discriminant”, Sb. Math., 206:2 (2015), 282–310  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. E. N. Mikhalkin, “The monodromy of a general algebraic function”, Siberian Math. J., 56:2 (2015), 330–338  mathnet  crossref  mathscinet  isi  elib  elib
    11. 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  crossref  mathscinet  zmath  isi  scopus
    12. I.A. Antipova, T.V. Zykova, “Mellin transforms and algebraic functions”, Integral Transforms and Special Functions, 2015, 1  crossref  mathscinet  scopus
    13. Beukers F., “Monodromy of A-hypergeometric functions”, J. Reine Angew. Math., 718 (2016), 183–206  crossref  mathscinet  zmath  isi  scopus
    14. 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  mathnet  crossref
    15. I. A. Antipova, “On the Structure of the Bochner–Martinelli Residue Currents”, Proc. Steklov Inst. Math., 298 (2017), 1–12  mathnet  crossref  crossref  isi  elib
    16. 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  mathnet  crossref  crossref  isi  elib  elib
    17. 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  mathnet  crossref
    18. 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  mathnet  crossref
    19. 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  mathnet  crossref
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