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Integration of Solutions of Linear Functional Equations Sergei A. Abramov #
 

Summary: Integration of Solutions of Linear Functional Equations
Sergei A. Abramov #
Computer Center of
the Russian Academy of Science,
Vavilova 40, Moscow 117967, Russia
abramov@ccas.ru
sabramov@cs.msu.su
Mark van Hoeij
Department of mathematics
Florida State University,
Tallahassee, FL 32306­3027, USA
hoeij@math.fsu.edu
Abstract
We introduce the notion of the adjoint Ore ring and give a definition of adjoint polynomial,
operator and equation. We apply this for integrating solutions of Ore equations.
1 Introduction
The goal of this paper is integration (in the di#erence case: summation) of solutions of Ore equations.
For this purpose we first define an adjoint for an Ore ring, similar to the well­known adjoint for di#erential
operators, and also similar to ideas in [10]. The use of Ore rings allows to handle the case of di#erential,
di#erence and q­di#erence equations simultaneously.

  

Source: Abramov, Sergei A. - Dorodnicyn Computing Centre of the Russian Academy of Sciences

 

Collections: Mathematics; Computer Technologies and Information Sciences