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 |
|---|---|
| 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 |
|---|---|
| Volume | 272 |
| ISSN (Print) | 0255-0156 |
| ISSN (Electronic) | 2296-4878 |
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Keywords
- Essential spectrum
- Spectrum
- Unbounded toeplitz operator
Cite this
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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.
Interpolation and Realization Theory with Applications to Control Theory: In honor of Joe Ball. ed. / V. Bolotnikov; S. ter Horst; A.C.M. Ran; V. Vinnikov. Springer International Publishing AG, 2019. p. 133-154 (Operator Theory: Advances and Applications; Vol. 272).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 -