The Schur Algorithm, Reproducing Kernel Spaces, and System Theory

Daniel Alpay, Stephen S. Wilson (Translator)

Research output: Book/ReportBookpeer-review

Abstract

The same positive functions (in the sense of reproduction kernel spaces) appear in a natural way in two different domains, namely the modeling of time-invariant dissipative linear systems and the theory of linear operators. We use the associated reproducing kernal Hilbert spaces to study the relationships between these domains. The inverse scattering problem plays a key role in the exposition. The reproducing kernel approach allows us to tackle in a natural way more general cases, such as nonstationary systems, the case of a non-positive metric and the case of pairs of commuting nonself-adjoint operators.
Original languageEnglish
Place of PublicationProvidence, R.I
PublisherAmerican Mathematical Society
Number of pages150
ISBN (Print)0821821555
StatePublished - 2001

Publication series

NameSMF/AMS texts and monographs
PublisherAmerican Mathematical Society
Volume5
ISSN (Print)1525-2303

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