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

118 Downloads (Pure)

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 - 1 Jan 2019

Publication series

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

Keywords

Essential spectrum
Spectrum
Unbounded toeplitz operator

Access to Document

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

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

Handle.net

Persistent link

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. 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).

@inbook{83e3f5d661ad4fcc874b2c2b5f9472aa,

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

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.",

keywords = "Essential spectrum, Spectrum, Unbounded toeplitz operator",

author = "Groenewald, {G. J.} and {ter Horst}, S. and J. Jaftha and Ran, {A. C.M.}",

year = "2019",

month = jan,

day = "1",

doi = "10.1007/978-3-030-11614-9_7",

language = "English",

isbn = "9783030116132",

series = "Operator Theory: Advances and Applications",

publisher = "Springer International Publishing AG",

pages = "133--154",

editor = "V. Bolotnikov and {ter Horst}, S. and A.C.M. Ran and V. Vinnikov",

booktitle = "Interpolation and Realization Theory with Applications to Control Theory",

address = "Switzerland",

}

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

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

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

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

AN - SCOPUS:85064736031

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 -

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). 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

Abstract

Publication series

Keywords

Access to Document

Handle.net

Other files and links

Fingerprint

Cite this