On Boundary Interpolation for Matrix Valued Schur Functions

• Author(s): Vladimir Bolotnikov, Harry Dym,
• Publisher: American Mathematical Soc.
• Pages: 107
• ISBN_10: 0821840479
  ISBN_13: 9780821840474
  
• Language: en
• Categories: Mathematics / Calculus , Mathematics / Differential Equations / General , Mathematics / Transformations , Mathematics / Complex Analysis ,

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.