Local analytic classification of q-difference equations with |q| = 1
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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We present algorithm qHyper for finding all solutions y(x) of a linear homogeneous q-difference equation, such that y(qx) = r(x)y(x) where r(x) is a rational function of x. Applications include construction of basic hypergeometric series solutions, and definite q-hypergeometric summation in closed form. ∗The research described in this publication was made possible in part by Grant J12100 from t...
متن کاملar X iv : 0 80 2 . 42 23 v 1 [ m at h . Q A ] 2 8 Fe b 20 08 Local analytic classification of q - difference equations
3 Analytic classification of admissible q-difference modules 10 3.1 Generalities on q-difference modules . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Simple objects in the category of admissible q-difference modules . . . . . . . 11 3.3 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Analytic vs formal classification . . . . . . . . . . . . ...
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2 Analytic factorization of q-difference operators 7 2.1 The Newton polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Admissible q-difference operators . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Analytic factorization of admissible q-difference operators . . . . . . . . . . . 9 2.4 A digression on formal factorization of q-difference operators . . . . . ...
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In this paper we extend the umbral calculus, developed to deal with difference equations on uniform lattices, to q-difference equations. We show that many of the properties considered for shift invariant difference operators satisfying the umbral calculus can be implemented to the case of the q-difference operators. This qumbral calculus can be used to provide solutions to linear q-difference e...
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ژورنال
عنوان ژورنال: Journal of Noncommutative Geometry
سال: 2009
ISSN: 1661-6952
DOI: 10.4171/jncg/33