✦ LIBER ✦
On rank invariance of generalized Schwarz–Pick–Potapov block matrices of matrix-valued Carathéodory functions
✍ Scribed by Andreas Lasarow
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 261 KB
- Volume
- 413
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
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. We derive statements on rank invariance of such generalized Schwarz-Pick-Potapov block matrices. These results are applied to describe the case of exactly one solution for the finite multiple Nevanlinna-Pick interpolation problem and to discuss matrix-valued Carathéodory functions with the highest degree of degeneracy.