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- W4387148113 abstract "This paper is a continuation of the work on unbounded Toeplitz-like operators $T_Om$ with rational matrix symbol $Om$ initiated in Groenewald et. al (Complex Anal. Oper. Theory 15, 1(2021)), where a Wiener-Hopf type factorization of $Om$ is obtained and used to determine when $T_Om$ is Fredholm and compute the Fredholm index in case $T_Om$ is Fredholm. Due to the high level of non-uniqueness and complicated form of the Wiener-Hopf type factorization, it does not appear useful in determining when $T_Om$ is invertible. In the present paper we use state space methods to characterize invertibility of $T_Om$ in terms of the existence of a stabilizing solution of an associated nonsymmetric discrete algebraic Riccati equation, which in turn leads to a pseudo-canonical factorization of $Om$ and concrete formulas of $T_Om^{-1}$." @default.
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- W4387148113 date "2023-09-26" @default.
- W4387148113 modified "2023-10-18" @default.
- W4387148113 title "A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: Invertibility and Riccati equations" @default.
- W4387148113 doi "https://doi.org/10.48550/arxiv.2309.14698" @default.
- W4387148113 hasPublicationYear "2023" @default.
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