Analytic theory of difference equations with rational and elliptic coefficients and the Riemann-Hilbert problem

Details Analytic theory of difference equations with rational and elliptic coefficients and the Riemann-Hilbert problem Analytic theory of difference equations with rational and elliptic coefficients and the Riemann-Hilbert problem

2004-07-10

arxiv.org/abs/math-ph/0407018v2

Physics

Mathematical Physics

38 pages, no figures; typos removed

Scientific paper

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.

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