Premium
An Operator Theoretic Approach to Degenerated Nevanlinna‐Pick Interpolation
Author(s) -
Woracek Harald
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951760124
Subject(s) - mathematics , algebra over a field , operator (biology) , calculus (dental) , interpolation (computer graphics) , pure mathematics , computer science , artificial intelligence , medicine , motion (physics) , biochemistry , chemistry , dentistry , repressor , transcription factor , gene
In this paper we consider an interpolation problem of Nevanlinna-Pick type: If finitely many points z1, . . . , zn of the open upper half plane C + are given, we study the existence of functions f ∈ Nν assuming prescribed values w1, . . . , wn ∈ C in these points: f(zi) = wi for i = 1, . . . , n. (1) Furthermore a description of all solutions of (1) through selfadjoint extensions of a certain symmetric operator is given. We recall the definition of the classes Nν . If f is a complex function denote by ρ(f) the domain of holomorphy of f . Definition 1 Let π and ν be nonnegative integers or ∞. Denote by Nν the set of all functions f which are meromorphic in C, such that the kernel