Journal of Siberian Federal University. Mathematics & Physics / On the Asymptotic of Homological Solutions to Linear Multidimensional Difference Equations

Full text (.pdf)
Issue
Journal of Siberian Federal University. Mathematics & Physics. 2014 7 (4)
Authors
Bushueva, Natalia A.; Kuzvesov, Konstantin V.; Tsikh, Avgust K.
Contact information
Bushueva, Natalia A.:Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia; ; Kuzvesov, Konstantin V.:Multifunctional Center 9 May, 12, Krasnoyarsk, 660125 Russia;; Tsikh, Avgust K.:Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia;
Keywords
difference equation; asymptotic; amoebas of algebraic sets; logarithmic Gauss map
Abstract

Given a linear homogeneous multidimensional difference equation with constant coefficients, we choose a pair ( , !), where is a homological k-dimensional cycle on the characteristic set of the equation and ! is a holomorphic form of degree k. This pair defines a so called homological solution by the integral over of the form ! 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

Pages
417–430
Paper at repository of SibFU
https://elib.sfu-kras.ru/handle/2311/16490