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On boundary interpolation for matrix valued Schur functions / Vladimir Bolotnikov, Harry Dym.
- Format:
- Book
- Author/Creator:
- Bolotnikov, Vladimir, 1962- author.
- Dym, H. (Harry), 1938- author.
- Series:
- Memoirs of the American Mathematical Society ; no. 856.
- Memoirs of the American Mathematical Society, 0065-9266 ; number 856
- Language:
- English
- Subjects (All):
- Schur functions.
- Interpolataion spaces.
- Moment problems (Mathematics).
- Lyapunov functions.
- Physical Description:
- 1 online resource (122 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2006]
- Language Note:
- English
- Summary:
- 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.
- Contents:
- ""Bibliography""
- Notes:
- "Volume 181, number 856 (end of volume)."
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
- 1-4704-0460-5
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