Green's Functions of Recurrence Relations with Reflection

TL;DR

This paper develops an algebraic framework for solving linear recurrence relations with reflection, providing explicit solutions, Green's functions, and exploring their relation to differential operators.

Contribution

It introduces a novel algebraic approach to recurrence relations with reflection, including explicit solutions and Green's functions, and compares them to differential operator algebras.

Findings

Explicit solutions and Green's functions for recurrence relations with reflection

Relations established between recurrence and differential operator algebras

Analysis of boundary conditions in recurrence problems

Abstract

In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear boundary conditions. Furthermore, we establish different relations between the algebras of recurrence and differential operators, showing the similarities and differences between them.