The twofold ellis–gohberg inverse problem in an abstract setting and applications

S. ter Horst*, M. A. Kaashoek, F. van Schagen

*Corresponding author for this work

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

Abstract

In this paper we consider a twofold Ellis–Gohberg type inverse problem in an abstract *-algebraic setting. Under natural assumptions, necessary and sufficient conditions for the existence of a solution are obtained, and it is shown that in case a solution exists, it is unique. The main result relies strongly on an inversion formula for a 2 × 2 block operator matrix whose off diagonal entries are Hankel operators while the diagonal entries are identity operators. Various special cases are presented, including the cases of matrixvalued L 1 -functions on the real line and matrix-valued Wiener functions on the unit circle of the complex plane. For the latter case, it is shown how the results obtained in an earlier publication by the authors can be recovered.

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
Pages155-212
Number of pages58
ISBN (Electronic)9783030116149
ISBN (Print)9783030116132
DOIs
Publication statusPublished - 2019

Publication series

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

Keywords

  • Abstract Toeplitz and Hankel operators
  • Integral operators
  • Inverse problem
  • Operator inversion
  • Wiener functions

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