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9780821840474

On Boundary Interpolation for Matrix Valued Schur Functions

by ;
  • ISBN13:

    9780821840474

  • ISBN10:

    0821840479

  • Format: Paperback
  • Copyright: 2006-04-30
  • Publisher: Amer Mathematical Society

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Summary

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 isalso considered.

Table of 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
Table of Contents provided by Publisher. All Rights Reserved.

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