A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: Fredholm properties
Date
2021Author
Groenewald, G.J.
Ter Horst, S.
Ran, A.C.M.
Jaftha, J.
Metadata
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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 Groenewald et al. (Oper Theory Adv Appl 271:239–268, 2018; Oper Theory Adv Appl 272:133–154, 2019; Integr Equ Oper Theory 91, 2019). 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
URI
http://hdl.handle.net/10394/36382https://link.springer.com/article/10.1007/s11785-020-01040-z
https://doi.org/10.1007/s11785-020-01040-z