On Boundary Interpolation for Matrix Valued Schur Functions

Released on by Vladimir Bolotnikov
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  • On Boundary Interpolation for Matrix Valued Schur Functions Book Detail

  • Author : Vladimir Bolotnikov
  • Release Date : 2006
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 122
  • ISBN 13 : 0821840479
  • File Size : 80,80 MB
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On Boundary Interpolation for Matrix Valued Schur Functions by Vladimir Bolotnikov PDF Summary

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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Topics In Interpolation Theory

Topics In Interpolation Theory

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