Spectral types of linear $q$-difference equations and $q$-analog of middle convolution
Classical Analysis and ODEs
2015-05-05 v3
Abstract
We give a -analog of middle convolution for linear -difference equations with rational coefficients. In the differential case, middle convolution is defined by Katz, and he examined properties of middle convolution in detail. In this paper, we define a -analog of middle convolution. Moreover, we show that it also can be expressed as a -analog of Euler transformation. The -middle convolution transforms Fuchsian type equation to Fuchsian type equation and preserves rigidity index of -difference equations.
Keywords
Cite
@article{arxiv.1410.3674,
title = {Spectral types of linear $q$-difference equations and $q$-analog of middle convolution},
author = {Hidetaka Sakai and Masashi Yamaguchi},
journal= {arXiv preprint arXiv:1410.3674},
year = {2015}
}