Analytic theory of difference equations with rational and elliptic coefficients and the Riemann-Hilbert problem
Mathematical Physics
2015-06-26 v2 High Energy Physics - Theory
Algebraic Geometry
Classical Analysis and ODEs
math.MP
Abstract
A new approach to the analytic theory of difference equations with rational and elliptic coefficients is proposed. It is based on the construction of canonical meromorphic solutions which are analytical along "thick paths". The concept of such solutions leads to a notion of local monodromies of difference equations. It is shown that in the continuous limit they converge to the monodromy matrices of differential equations. New type of isomonodromic deformations of difference equations with elliptic coefficients changing the periods of elliptic curves is constructed.
Keywords
Cite
@article{arxiv.math-ph/0407018,
title = {Analytic theory of difference equations with rational and elliptic coefficients and the Riemann-Hilbert problem},
author = {I. Krichever},
journal= {arXiv preprint arXiv:math-ph/0407018},
year = {2015}
}
Comments
38 pages, no figures; typos removed