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

Research output: Chapter in Book / Report / Conference proceedingChapterAcademicpeer-review

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 languageEnglish
Title of host publicationInterpolation and Realization Theory with Applications to Control Theory
Subtitle of host publicationIn honor of Joe Ball
EditorsV. Bolotnikov, S. ter Horst, A.C.M. Ran, V. Vinnikov
PublisherSpringer International Publishing AG
Pages133-154
Number of pages22
ISBN (Electronic)9783030116149
ISBN (Print)9783030116132
DOIs
Publication statusPublished - 1 Jan 2019

Publication series

NameOperator Theory: Advances and Applications
Volume272
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Fingerprint

Essential Spectrum
Otto Toeplitz
Unit circle
Pole
Continuous Spectrum
Operator
Continuation
Class

Keywords

  • Essential spectrum
  • Spectrum
  • Unbounded toeplitz operator

Cite this

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. ; Ran, A. C.M. / 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.; 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 proceedingChapterAcademicpeer-review

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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). https://doi.org/10.1007/978-3-030-11614-9_7