Carathéodory matrix-valued function, multiple point Nevanlinna-Pick interpolation problem, trigonometric matrix moment problem, block Toeplitz vector, block Pick matrix, block Toeplitz matrix MSC (2010) 30E05, 47A56 The main theme of this paper is a study of a multiple point Nevanlinna-Pick type in
On boundary Nevanlinna–Pick interpolation for Carathéodory matrix functions
✍ Scribed by Yong-Jian Hu; K.d.A. Boubakar; Gong-Ning Chen
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 247 KB
- Volume
- 423
- Category
- Article
- ISSN
- 0024-3795
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## Abstract We consider an interpolation problem of Nevanlinna–Pick type for matrix‐valued Carathéodory functions, where the values of the functions and its derivatives up to certain orders are given at finitely many points of the open unit disk. For the non‐degenerate case, i.e., in the particular
In view of a multiple Nevanlinna-Pick interpolation problem, we study the rank of generalized Schwarz-Pick-Potapov block matrices of matrix-valued Carathéodory functions. Those matrices are determined by the values of a Carathéodory function and the values of its derivatives up to a certain order. W
## Abstract We solve a boundary interpolation problem at a real point for generalized Nevanlinna functions, and use the result to prove uniqueness theorems for generalized Nevanlinna functions (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)