Summary: Integration of Solutions of Linear Functional Equations
Sergei A. Abramov #
Computer Center of
the Russian Academy of Science,
Vavilova 40, Moscow 117967, Russia
Mark van Hoeij
Department of mathematics
Florida State University,
Tallahassee, FL 323063027, USA
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.
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 . The use of Ore rings allows to handle the case of di#erential,
di#erence and qdi#erence equations simultaneously.