On Boundary Interpolation for Matrix Valued Schur Functions PDF Download

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On Boundary Interpolation for Matrix Valued Schur Functions

On Boundary Interpolation for Matrix Valued Schur Functions PDF Author: Vladimir Bolotnikov
Publisher: American Mathematical Soc.
ISBN: 0821840479
Category : Mathematics
Languages : en
Pages : 122

Book 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 isalso considered.
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