Building Meromorphic Solutions ofq-Difference Equations Using a Borel–Laplace Summation
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Publication:3450445
DOI10.1093/imrn/rnu137zbMath1357.39007arXiv1401.4564OpenAlexW2158404710MaRDI QIDQ3450445
Publication date: 5 November 2015
Published in: International Mathematics Research Notices (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1401.4564
Newton polygontheta function\(q\)-difference equationmeromorphic solution\(q\)-Laplace transformformal power series solutionlinear \(q\)-difference system\(q\)-Borel transform
Difference equations, scaling ((q)-differences) (39A13) Linear difference equations (39A06) Difference equations in the complex domain (39A45)
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The \(q\)-Borel sum of divergent basic hypergeometric series \(_r\phi_s(a;b;q,x)\) ⋮ Isomonodromic deformation of 𝑞-difference equations and confluence ⋮ q-Analogues of Laplace and Borel transforms by means of q-exponentials ⋮ Meromorphic solutions of linear \(q\)-difference equations ⋮ q-Borel-Laplace summation for q–difference equations with two slopes ⋮ On sequences preserving \(q\)-Gevrey asymptotic expansions ⋮ \(q\)-deformation of meromorphic solutions of linear differential equations ⋮ On parametric multilevel \(q\)-Gevrey asymptotics for some linear \(q\)-difference-differential equations ⋮ Galois theories of \(q\)-difference equations: comparison theorems ⋮ Zeros, growth and Taylor coefficients of entire solutions of linear q-difference equations ⋮ Solutions of a class of multiplicatively advanced differential equations. II: Fourier transforms ⋮ On the multiple-scale analysis for some linear partial \(q\)-difference and differential equations with holomorphic coefficients
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