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This article is cited in 17 scientific papers (total in 17 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.
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
Linking options:
https://www.mathnet.ru/eng/rm798https://doi.org/10.1070/RM2004v059n06ABEH000798 https://www.mathnet.ru/eng/rm/v59/i6/p111
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Abstract page: | 1055 | Russian version PDF: | 382 | English version PDF: | 33 | References: | 101 | First page: | 4 |
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