منابع مشابه
Galois theory of fuchsian q-difference equations
We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff’s classification scheme with the connection matrix to define and describe their Galois groups. Then we describe fundamental subgroups that give rise to a Riemann-Hilbert correspondence and to a density theorem of Schlesinger’s type.
متن کاملσ-Galois theory of linear difference equations
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 ...
متن کاملGALOIS GROUPS AND CONNECTION MATRICES OF q-DIFFERENCE EQUATIONS
We study the Galois group of a matrix q-difference equation with rational coefficients which is regular at 0 and ∞, in the sense of (difference) Picard-Vessiot theory, and show that it coincides with the algebraic group generated by matrices C(u)C(w)−1 u,w ∈ C∗ , where C(z) is the Birkhoff connection matrix of the equation. 1. Differential algebra The notion of the Galois group of a linear ordi...
متن کاملNevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations
It is shown that, if f is a meromorphic function of order zero and q ∈ C, then m „ r, f(qz) f(z) « = o(T (r, f)) (‡) for all r on a set of logarithmic density 1. The remainder of the paper consist of applications of identity (‡) to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of q-difference equations. The results obta...
متن کاملAnalytic 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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ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 2007
ISSN: 0240-2963
DOI: 10.5802/afst.1164