Multi-Point Degenerate Interpolation Problem for Generalized Schur Functions: Description of All Solutions
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- 作者：Vladimir Bolotnikov (1)
- 关键词：Generalized Schur functions ; Nevanlinna ; Pick ; Carathéodory ; Fejér interpolation problem ; Pick matrix ; 30E05
- 刊名：Computational Methods and Function Theory
- 出版年：2011
- 出版时间：September 2011
- 年：2011
- 卷：11
- 期：1
- 页码：143-160
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1. Department of Mathematics, The College of William and Mary, Williamsburg, VA, 23187-8795, USA - ISSN：2195-3724
文摘
We consider the Nevanlinna-Pick-Carathéodory-Fejér interpolation problem with finitely many interpolation conditions in the class S gk of meromorphic functions f with ?em class="a-plus-plus">f?sub class="a-plus-plus">l ?/sup> (t) ?1 and with κ poles inside the unit disk D. The problem has infinitely many solutions if and only if κ is greater than or equal to the number of non-positive eigenvalues (counted with multiplicities) of the Pick matrix P constructed from interpolation data. For each such κ, we describe the solution set of the problem in terms of a family of linearfractional transformations with disjoint ranges. The parameters defining this family are free and independent.