A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: Fredholm properties
Functional Analysis
2020-06-01 v1
Abstract
This paper concerns the analysis of an unbounded Toeplitz-like operator generated by a rational matrix function having poles on the unit circle T. It extends the analysis of such operators generated by scalar rational functions with poles on T found in [11,12,13]. A Wiener-Hopf type factorization of rational matrix functions with poles and zeroes on T is proved and then used to analyze the Fredholm properties of such Toeplitz-like operators. A formula for the index, based on the factorization, is given. Furthermore, it is shown that the determinant of the matrix function having no zeroes on T is not sufficient for the Toeplitz-like operator to be Fredholm, in contrast to the classical case.
Keywords
Cite
@article{arxiv.2005.14561,
title = {A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: Fredholm properties},
author = {G. J. Groenewald and S. ter Horst and J. Jaftha and A. C. M. Ran},
journal= {arXiv preprint arXiv:2005.14561},
year = {2020}
}
Comments
25 pages