A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: Fredholm properties
| Autor: | Groenewald, G. J., ter Horst, S., Jaftha, J., Ran, A. C. M. |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 25 pages |
| Databáze: | arXiv |
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