Spectral types of linear q-difference equations and q-analog of middle convolution

2014/10/14 by Hidetaka Sakai, Sakai, Hidetaka, Masashi Yamaguchi +1
Computer Science · Mathematics · Physics and Astronomy · #33D15 #39A13 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1410.3674

openalex publication_date 2014/10/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We give a q-analog of middle convolution for linear q-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 q-analog of middle convolution. Moreover, we show that it also can be expressed as a q-analog of Euler transformation. The q-middle convolution transforms Fuchsian type equation to Fuchsian type equation and preserves rigidity index of q-difference equations.

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