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J. Sib. Fed. Univ. Math. Phys., 2014, Volume 7, Issue 4, Pages 417–430 (Mi jsfu388)  

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

On the asymptotic of homological solutions to linear multidimensional difference equations

Natalia A. Bushuevaa, Konstantin V. Kuzvesovb, Avgust K. Tsikha

a Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia
b Multifunctional Center, 9 May, 12, Krasnoyarsk, 660125, Russia

Abstract: Given a linear homogeneous multidimensional difference equation with constant coefficients, we choose a pair $(\gamma,\omega)$, where $\gamma$ is a homological $k$-dimensional cycle on the characteristic set of the equation and $\omega$ is a holomorphic form of degree $k$. This pair defines a so called homological solution by the integral over $\gamma$ of the form $\omega$ multiplied by an exponential kernel. A multidimensional variant of Perron's theorem in the class of homological solutions is illustrated by an example of the first order equation.

Keywords: difference equation, asymptotic, amoebas of algebraic sets, logarithmic Gauss map.

Full text: PDF file (265 kB)
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UDC: 517.55
Received: 18.08.2014
Received in revised form: 25.09.2014
Accepted: 20.10.2014
Language:

Citation: Natalia A. Bushueva, Konstantin V. Kuzvesov, Avgust K. Tsikh, “On the asymptotic of homological solutions to linear multidimensional difference equations”, J. Sib. Fed. Univ. Math. Phys., 7:4 (2014), 417–430

Citation in format AMSBIB
\Bibitem{BusKuzTsi14}
\by Natalia~A.~Bushueva, Konstantin~V.~Kuzvesov, Avgust~K.~Tsikh
\paper On the asymptotic of homological solutions to linear multidimensional difference equations
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2014
\vol 7
\issue 4
\pages 417--430
\mathnet{http://mi.mathnet.ru/jsfu388}


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    This publication is cited in the following articles:
    1. Mikhalkin E.N., Shchuplev A.V., Tsikh A.K., “Amoebas of Cuspidal Strata For Classical Discriminant”, Complex Analysis and Geometry, Kscv 10, Springer Proceedings in Mathematics & Statistics, 144, eds. Bracci F., Byun J., Gaussier H., Hirachi K., Kim K., Shcherbina N., Springer, 2015, 257–272  crossref  mathscinet  zmath  isi  scopus
    2. Valery V. Denisenko, Vladimir M. Sadovskii, Sergey S. Zamay, “Mathematical modeling of the impact produced by magnetic disks on living cells”, Zhurn. SFU. Ser. Matem. i fiz., 9:4 (2016), 432–442  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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