A toeplitz-like operator with rational symbol having poles on the unit circle i: Fredholm properties

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

*Corresponding author for this work

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

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Abstract

In this paper a definition is given for an unbounded Toeplitzlike operator with rational symbol which has poles on the unit circle. It is shown that the operator is Fredholm if and only if the symbol has no zeroes on the unit circle, and a formula for the index is given as well. Finally, a matrix representation of the operator is discussed.

Original languageEnglish
Title of host publicationOperator Theory, Analysis and the State Space Approach
Subtitle of host publicationIn Honor of Rien Kaashoek
PublisherSpringer International Publishing Switzerland
Pages239-268
Number of pages30
ISBN (Electronic)9783030042691
ISBN (Print)9783030042684
DOIs
Publication statusPublished - 2018

Publication series

NameOperator Theory: Advances and Applications
Volume271
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

  • Fredholm properties
  • Toeplitz operators
  • Unbounded operators

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