An interpolation problem for functions with values in a commutative ring

TL;DR

This paper explores an interpolation problem within the framework of linear systems over a commutative ring of power series, leveraging algebraic identities to extend system theory concepts.

Contribution

It introduces an interpolation problem in the context of linear systems on a commutative ring, expanding the theoretical foundation of system analysis in algebraic settings.

Findings

Established conditions for interpolation in the ring-based system framework

Demonstrated the applicability of algebraic identities in system interpolation

Extended classical system theory to algebraic structures beyond fields

Abstract

It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we study an interpolation problem in this setting. A key tool is the principle of permanence of algebraic identities.