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On Boundary Interpolation for Matrix Valued Schur Functions
Vladimir BolotnikovHarry Dym
出版American Mathematical Soc., 2006
主題Mathematics / CalculusMathematics / Differential Equations / GeneralMathematics / TransformationsMathematics / Complex Analysis
ISBN08218404799780821840474
URLhttp://books.google.com.hk/books?id=1krVCQAAQBAJ&hl=&source=gbs_api
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註釋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.