Convolution equations and linear systems

Abstract

This paper developes further the connections between linear systems and convolution equations. Here the emphasis is on equations on finite intervals. For these equations a new characteristic matrix (or operator) function is introduced, which contains all the important information about the equations and the corresponding operators. Explicit formulas for solutions and resolvent kernels are obtained. Convolution equations on the full line are also analyzed. Analogous results are derived for the inversion of finite and infinite Toeplitz matrices.