The boundary Carathéodory–Fejér interpolation problem

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• 作者：Jim Agler^a ; Zinaida A. Lykova^b ; ^{z.a.lykova@ncl.ac.uk"" rel=""nofollow} ; N.J. Young^c
• 关键词：Pick class ; Boundary interpolation ; Parametrization ; Hankel matrix ; Schur complement
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2011
• 出版时间：15 October 2011
• 年：2011
• 卷：382
• 期：2
• 页码：645-662
• 全文大小：272 K

文摘

We give a new solvability criterion for the boundary Carathéodory–Fejér problem: given a point and, a finite set of target values, to construct a function f in the Pick class such that the first few derivatives of f take on the prescribed target values at x. We also derive a linear fractional parametrization of the set of solutions of the interpolation problem with real target values. The proofs are based on a reduction method due to Julia and Nevanlinna.