Analytic theory of linear q-difference equations
نویسندگان
چکیده
منابع مشابه
Analytic q-difference equations
A complex number q with 0 < |q| < 1 is fixed. By an analytic q-difference equation we mean an equation which can be represented by a matrix equation Y (z) = A(z)Y (qz) where A(z) is an invertible n× n-matrix with coefficients in the field K = C({z}) of the convergent Laurent series and where Y (z) is a vector of size n. The aim of this paper is to give an overview of our present knowledge of th...
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— The words “monodromy” and “isomonodromy” are used in the theory of difference and q-difference equations by Baranovsky-Ginzburg, Jimbo-Sakai, Borodin, Krichever,... although it is not clear that phenomena of branching during analytic continuation are involved there. In order to clarify what is at stake, we survey results obtained during the last few years, mostly by J.-P. Ramis, J. Sauloy and...
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Inspired by the numerous applications of the differential algebraic independence results from [36], we develop a Galois theory with an action of an endomorphism σ for systems of linear difference equations of the form φ(y) = Ay , where A ∈ GLn(K ) and K is a φσ-field, that is, a field with two given commuting endomorphisms φ and σ, like in Example 2.1. This provides a technique to test whether ...
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1933
ISSN: 0001-5962
DOI: 10.1007/bf02547785