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OverviewWe present a multivariable setting for Lax-Phillips scattering and for conservative, discrete-time, linear systems. The evolution operator for the Lax-Phillips scattering system is an isometric representation of the Cuntz algebra, while the nonnegative time axis for the conservative, linear system is the free semigroup on $d$ letters. The correspondence between scattering and system theory and the roles of the scattering function for the scattering system and the transfer function for the linear system are highlighted.Another issue addressed in this title is the extension of a given representation of the Cuntz-Toeplitz algebra (i.e., a row isometry) to a representation of the Cuntz algebra (i.e., a row unitary); the solution to this problem relies on an extension of the Szego factorization theorem for positive Toeplitz operators to the Cuntz-Toeplitz algebra setting. As an application, we obtain a complete set of unitary invariants (the characteristic function together with a choice of 'Haplitz' extension of the characteristic function defect) for a row-contraction on a Hilbert space. Full Product DetailsAuthor: Joseph A. Ball , Victor VinnikovPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 178 Weight: 0.227kg ISBN: 9780821837689ISBN 10: 0821837680 Pages: 101 Publication Date: 30 October 2005 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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