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This article is cited in 16 scientific papers (total in 16 papers)
Analytic theory of difference equations with rational and elliptic coefficients and the Riemann–Hilbert problem
I. M. Kricheverab
a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Columbia University
Abstract:
A new approach to the construction of the analytic theory of difference equations with rational and elliptic coefficients is proposed, based on the construction of canonical meromorphic
solutions which are analytic along “thick” paths. The concept of these solutions leads to the definition of local monodromies of difference equations. It is shown that, in the continuous limit,
these local monodromies converge to monodromy matrices of differential equations. In the elliptic case a new type of isomonodromy transformations changing the periods of
elliptic curves is constructed.
DOI:
https://doi.org/10.4213/rm798
 Full text:
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English version:
Russian Mathematical Surveys, 2004, 59:6, 1117–1154
Bibliographic databases:
    
UDC:
517.9
MSC: Primary 30E25, 39A11, 34M35; Secondary 34M50, 34M55, 45E05, 30D99, 32S40, 14H52
Received: 28.06.2004
Citation:
I. M. Krichever, “Analytic theory of difference equations with rational and elliptic coefficients and the Riemann–Hilbert problem”, Uspekhi Mat. Nauk, 59:6(360) (2004), 111–150; Russian Math. Surveys, 59:6 (2004), 1117–1154
Citation in format AMSBIB
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