Memoirs of the American Mathematical Society 2006; 107 pp; softcover Volume: 181 ISBN10: 0821840479 ISBN13: 9780821840474 List Price: US$61 Individual Members: US$36.60 Institutional Members: US$48.80 Order Code: MEMO/181/856
 A number of interpolation problems are considered in the Schur class of \(p\times q\) matrix valued functions \(S\) that are analytic and contractive in the open unit disk. The interpolation constraints are specified in terms of nontangential limits and angular derivatives at one or more (of a finite number of) boundary points. Necessary and sufficient conditions for existence of solutions to these problems and a description of all the solutions when these conditions are met is given. The analysis makes extensive use of a class of reproducing kernel Hilbert spaces \({\mathcal{H}}(S)\) that was introduced by de Branges and Rovnyak. The Stein equation that is associated with the interpolation problems under consideration is analyzed in detail. A lossless inverse scattering problem is also considered. Table of Contents  Introduction
 Preliminaries
 Fundamental matrix inequalities
 On \(\mathcal{H}(\Theta)\) spaces
 Parametrizations of all solutions
 The equality case
 Nontangential limits
 The NevanlinnaPick boundary problem
 A multiple analogue of the CarathéodoryJulia theorem
 On the solvability of a Stein equation
 Positive definite solutions of the Stein equation
 A CarathéodoryFejér boundary problem
 The full matrix CarathéodoryFejér boundary problem
 The lossless inverse scattering problem
 Bibliography
