A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: matrix representation and spectral analysis

Abstract

In this paper we consider a class of unbounded Toeplitz operators with rational matrix symbols that have poles on the unit circle and employ state space realization techniques from linear systems theory, as used in our earlier analysis in Groenewald et al. (J Math Anal Appl 532, Paper no. 127925, 2024) of this class of operators, to study the connection with semi-infinite Toeplitz matrices and to determine the essential spectrum and resolvent set.