Pseudo-Taylor expansions and the Carath¨¦odory¨CFej¨¦r problem

详细信息    查看全文

• 作者：Jim  ; Agler^a ; Zinaida A.  ; Lykova^b ;   ; ^{z.a.lykova@ncl.ac.uk} ; N.J.  ; Young^c
• 关键词：Pick class ; Boundary interpolation ; Hankel matrix ; Schur complement
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 出版时间：1 February 2012
• 年：2012
• 卷：386
• 期：1
• 页码：308-318
• 全文大小：199 K

文摘

We give a new solvability criterion for the boundary Carath¨¦odory¨CFej¨¦r problem: given a point and, a finite set of target values , to construct a function f in the Pick class such that the limit of as nontangentially in the upper half-plane is for . The criterion is in terms of positivity of an associated Hankel matrix. The proof is based on a reduction method due to Julia and Nevanlinna.