Title :

On q-summation and confluence

Author(s) :

Di Vizio, Lucia [Auteur]
Institut de Mathématiques de Jussieu [IMJ]
Zhang, Changgui [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Annales de l'Institut Fourier

Pages :

347-392

Publisher :

Association des Annales de l'Institut Fourier

Publication date :

2009

ISSN :

0373-0956

HAL domain(s) :

Mathématiques [math]/Analyse classique [math.CA]
Mathématiques [math]/Algèbres quantiques [math.QA]

English abstract : [en]

This paper is divided in two parts. In the first part we consider irregular singular analytic q-difference equations, with q\in ]0,1[, and we show how the Borel sum of a divergent solution of a differential equation can ...
Show more >This paper is divided in two parts. In the first part we consider irregular singular analytic q-difference equations, with q\in ]0,1[, and we show how the Borel sum of a divergent solution of a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of such a q-difference equation. In the second part, we work under the assumption q\in ]1,+\infty[. In this case, at least four different q-Borel sums of a divergent solution of an irregular singular analytic q-difference equations are spread in the literature: under convenient assumptions we clarify the relations among them.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Approche géométrique à l'approximation diophantienne

Comment :

36 pages. Following the referee's comments, we have clarified the exposition of some proofs and corrected some misprints

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL