Memoirs of the American Mathematical Society 2005; 101 pp; softcover Volume: 178 ISBN10: 0821837680 ISBN13: 9780821837689 List Price: US$66 Individual Members: US$39.60 Institutional Members: US$52.80 Order Code: MEMO/178/837
 We present a multivariable setting for LaxPhillips scattering and for conservative, discretetime, linear systems. The evolution operator for the LaxPhillips 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 is the extension of a given representation of the CuntzToeplitz 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 Szegö factorization theorem for positive Toeplitz operators to the CuntzToeplitz 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 rowcontraction on a Hilbert space. Readership Graduate students and research mathematicians interested in analysis. Table of Contents  Introduction
 Functional models for rowisometric/rowunitary operator tuples
 Cuntz scattering systems
 Unitary colligations
 Scattering, systems and dilation theory: the CuntzToeplitz setting
 Bibliography
