### Abstract

This paper is a continuation of our study of a class of Toeplitz-like operators with a rational symbol which has a pole on the unit circle. A description of the spectrum and its various parts, i.e., point, residual and continuous spectrum, is given, as well as a description of the essential spectrum. In this case, the essential spectrum need not be connected in C. Various examples illustrate the results.

Original language | English |
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Title of host publication | Interpolation and Realization Theory with Applications to Control Theory |

Subtitle of host publication | In honor of Joe Ball |

Editors | V. Bolotnikov, S. ter Horst, A.C.M. Ran, V. Vinnikov |

Publisher | Springer International Publishing AG |

Pages | 133-154 |

Number of pages | 22 |

ISBN (Electronic) | 9783030116149 |

ISBN (Print) | 9783030116132 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

### Publication series

Name | Operator Theory: Advances and Applications |
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Volume | 272 |

ISSN (Print) | 0255-0156 |

ISSN (Electronic) | 2296-4878 |

### Fingerprint

### Keywords

- Essential spectrum
- Spectrum
- Unbounded toeplitz operator

### Cite this

*Interpolation and Realization Theory with Applications to Control Theory: In honor of Joe Ball*(pp. 133-154). (Operator Theory: Advances and Applications; Vol. 272). Springer International Publishing AG. https://doi.org/10.1007/978-3-030-11614-9_7

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*Interpolation and Realization Theory with Applications to Control Theory: In honor of Joe Ball.*Operator Theory: Advances and Applications, vol. 272, Springer International Publishing AG, pp. 133-154. https://doi.org/10.1007/978-3-030-11614-9_7

**A toeplitz-like operator with rational symbol having poles on the unit circle II : The spectrum.** / Groenewald, G. J.; ter Horst, S.; Jaftha, J.; Ran, A. C.M.

Research output: Chapter in Book / Report / Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - A toeplitz-like operator with rational symbol having poles on the unit circle II

T2 - The spectrum

AU - Groenewald, G. J.

AU - ter Horst, S.

AU - Jaftha, J.

AU - Ran, A. C.M.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - This paper is a continuation of our study of a class of Toeplitz-like operators with a rational symbol which has a pole on the unit circle. A description of the spectrum and its various parts, i.e., point, residual and continuous spectrum, is given, as well as a description of the essential spectrum. In this case, the essential spectrum need not be connected in C. Various examples illustrate the results.

AB - This paper is a continuation of our study of a class of Toeplitz-like operators with a rational symbol which has a pole on the unit circle. A description of the spectrum and its various parts, i.e., point, residual and continuous spectrum, is given, as well as a description of the essential spectrum. In this case, the essential spectrum need not be connected in C. Various examples illustrate the results.

KW - Essential spectrum

KW - Spectrum

KW - Unbounded toeplitz operator

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UR - http://www.scopus.com/inward/citedby.url?scp=85064736031&partnerID=8YFLogxK

UR - https://www.springer.com/gp/book/9783030116132

U2 - 10.1007/978-3-030-11614-9_7

DO - 10.1007/978-3-030-11614-9_7

M3 - Chapter

SN - 9783030116132

T3 - Operator Theory: Advances and Applications

SP - 133

EP - 154

BT - Interpolation and Realization Theory with Applications to Control Theory

A2 - Bolotnikov, V.

A2 - ter Horst, S.

A2 - Ran, A.C.M.

A2 - Vinnikov, V.

PB - Springer International Publishing AG

ER -