# On Boundary Interpolation for Matrix Valued Schur Functions (Memoirs of the American Mathematical Society)

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### Description

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.

### Contents

Introduction Preliminaries Fundamental matrix inequalities On $\mathcal{H}(\Theta)$ spaces Parametrizations of all solutions The equality case Nontangential limits The Nevanlinna-Pick boundary problem A multiple analogue of the Caratheodory-Julia theorem On the solvability of a Stein equation Positive definite solutions of the Stein equation A Caratheodory-Fejer boundary problem The full matrix Caratheodory-Fejer boundary problem The lossless inverse scattering problem Bibliography.

### Product Details

• ISBN13: 9780821840474
• Format: Paperback
• Number Of Pages: 107
• ID: 9780821840474
• ISBN10: 0821840479

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