Factoring and decomposing a class of linear functional systems

Factoring and decomposing a class of linear functional systems

Within a constructive homological algebra approach, we study the factorization and decomposition problems for a class of linear functional (determined, over-determined, under-determined) systems. Using the concept of Ore algebras of functional operators (e.g., ordinary/partial differential operators, shift operators, time-delay operators), we first concentrate on the computation of morphisms fr...

Using morphism computations for factoring and decomposing general linear functional systems

Within a constructive homological algebra approach, we study the factorization and decomposition problems for general linear functional systems and, in particular, for multidimensional linear systems appearing in control theory. Using the concept of Ore algebras of functional operators (e.g., ordinary/partial differential operators, shift operators, time-delay operators), we first concentrate o...

Factoring Finite-rank Linear Functional Systems∗

By a finite-rank (linear functional) system, we mean a system of linear differential, shift and q-shift operators or, any mixture thereof, whose solution space is finite-dimensional. This poster attempts to develop an algorithm for factoring finite-rank systems into “subsystems” whose solution spaces are of lower dimension. This work consists of three parts: 1. using module-theoretic language t...

Explicit ABS Solution of a Class of Linear Inequality Systems and LP Problems

On the $c_{0}$-solvability of a class of infinite systems of functional-integral equations

  In this paper, an existence result for a class of infinite systems of functional-integral equations in the Banach sequence space $c_{0}$ is established via the well-known Schauder fixed-point theorem together with a criterion of compactness in the space $c_{0}$. Furthermore, we include some remarks to show the vastity of the class of infinite systems which can be covered by our result. The a...