A toeplitz-like operator with rational symbol having poles on the unit circle II: The spectrum

G. J. Groenewald; S. ter Horst; J. Jaftha; A. C.M. Ran

doi:10.1007/978-3-030-11614-9_7

A toeplitz-like operator with rational symbol having poles on the unit circle II: The spectrum

G. J. Groenewald^*, S. ter Horst, J. Jaftha, A. C.M. Ran

^*Corresponding author for this work

Mathematics

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

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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	https://doi.org/10.1007/978-3-030-11614-9_7
Publication status	Published - 2019

Publication series

Name	Operator Theory: Advances and Applications
Volume	272
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Funding

This work is based on the research supported in part by the National Research Foundation of South Africa (Grant Number 90670 and 93406). Part of the research was done during a sabbatical of the third author, in which time several research visits to VU Amsterdam and North-West University were made. Support from University of Cape Town and the Department of Mathematics, VU Amsterdam is gratefully acknowledged. The present work is based on research supported in part by the National Research Foundation of South Africa. Any opinion, finding and conclusion or recommendation expressed in this material is that of the authors and the NRF does not accept any liability in this regard. Acknowledgement. The present work is based on research supported in part by the National Research Foundation of South Africa. Any opinion, finding and conclusion or recommendation expressed in this material is that of the authors and the NRF does not accept any liability in this regard.

Funders	Funder number
National Research Foundation
National Research Foundation of South Africa	90670, 93406
National Research Foundation

Keywords

Essential spectrum
Spectrum
Unbounded toeplitz operator

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

Groenewald2019_Chapter_AToeplitz-likeOperatorWithRationalSymbolHavingFinal published version, 1.11 MBLicence: Article 25fa Dutch Copyright Act

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Groenewald, G. J., ter Horst, S., Jaftha, J., & Ran, A. C. M. (2019). A toeplitz-like operator with rational symbol having poles on the unit circle II: The spectrum. In V. Bolotnikov, S. ter Horst, A. C. M. Ran, & V. Vinnikov (Eds.), 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

Groenewald, G. J. ; ter Horst, S. ; Jaftha, J. et al. / A toeplitz-like operator with rational symbol having poles on the unit circle II: The spectrum. Interpolation and Realization Theory with Applications to Control Theory: In honor of Joe Ball. editor / V. Bolotnikov ; S. ter Horst ; A.C.M. Ran ; V. Vinnikov. Springer International Publishing AG, 2019. pp. 133-154 (Operator Theory: Advances and Applications).

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Groenewald, GJ, ter Horst, S, Jaftha, J & Ran, ACM 2019, A toeplitz-like operator with rational symbol having poles on the unit circle II: The spectrum. in V Bolotnikov, S ter Horst, ACM Ran & V Vinnikov (eds), 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. et al.
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

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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.

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Groenewald GJ, ter Horst S, Jaftha J, Ran ACM. A toeplitz-like operator with rational symbol having poles on the unit circle II: The spectrum. In Bolotnikov V, ter Horst S, Ran ACM, Vinnikov V, editors, Interpolation and Realization Theory with Applications to Control Theory: In honor of Joe Ball. Springer International Publishing AG. 2019. p. 133-154. (Operator Theory: Advances and Applications). Epub 2019 Apr 19. doi: 10.1007/978-3-030-11614-9_7

A toeplitz-like operator with rational symbol having poles on the unit circle II: The spectrum

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