A number of interpolation problems are considered in the Schur class of p x
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 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.
Received by the editor September 11, 1999 and, in revised form, September 22, 2003.
1991 Mathematics Subject Classification. 30E05, 446E22, 47A57.
Key words and phrases. Boundary interpolation, Lyapunov-Stein equation, matrix valued
Schur functions.
H. Dym thanks Renee and Jay Weiss for endowing the Chair that supports his research and
the Israel Science Foundation for support under grant 300/02.
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