dc.contributor.author | Groenewald, G.J. | |
dc.contributor.author | Ter Horst, S. | |
dc.contributor.author | Ran, A.C.M. | |
dc.contributor.author | Jaftha, J. | |
dc.date.accessioned | 2020-11-19T06:44:37Z | |
dc.date.available | 2020-11-19T06:44:37Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Groenewald, G.J. et al. 2021. A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: Fredholm properties. Complex analysis and operator theory, 15(1): art. #1. [https://doi.org/10.1007/s11785-020-01040-z] | en_US |
dc.identifier.issn | 1661-8254 | |
dc.identifier.issn | 1661-8262 (Online) | |
dc.identifier.uri | http://hdl.handle.net/10394/36382 | |
dc.identifier.uri | https://link.springer.com/article/10.1007/s11785-020-01040-z | |
dc.identifier.uri | https://doi.org/10.1007/s11785-020-01040-z | |
dc.description.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 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 | en_US |
dc.language.iso | en | en_US |
dc.publisher | Springer | en_US |
dc.subject | Toeplitz operators | en_US |
dc.subject | Unbounded operators | en_US |
dc.subject | Fredholm properties | en_US |
dc.subject | Rational matrix functions | en_US |
dc.subject | Wiener-Hopf factorization | en_US |
dc.title | A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: Fredholm properties | en_US |
dc.type | Article | en_US |
dc.contributor.researchID | 12066680 - Groenewald, Gilbert Joseph | |
dc.contributor.researchID | 24116327 - Ter Horst, Sanne | |
dc.contributor.researchID | 20000212 - Ran, Andreas Cornelis Maria | |