Solution of a multiple Nevanlinna–Pick problem for Carathéodory functions via orthogonal rational functions in the matrix case

2008 ◽  
Vol 281 (1) ◽  
pp. 75-108 ◽  
Author(s):  
Andreas Lasarow
Keyword(s):  
Rational Functions ◽  
Orthogonal Rational Functions ◽  
Carathéodory Functions ◽  
The Matrix ◽  
Pick Problem ◽  
Matrix Case

scholarly journals Solution of a multiple Nevanlinna–Pick problem for Schur functions via orthogonal rational functions

Analysis ◽  
2008 ◽  
Vol 28 (1) ◽  
Author(s):  
Adhemar Bultheel ◽  
Andreas Lasarow
Keyword(s):  
Unique Solution ◽  
Interpolation Problem ◽  
Schur Functions ◽  
Rational Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Orthogonal Rational Functions ◽  
All Solutions ◽  
Pick Problem ◽  
Complex Valued

An interpolation problem of Nevanlinna–Pick type for complex-valued Schur functions in the open unit disk is considered. We prescribe the values of the function and its derivatives up to a certain order at finitely many points. Primarily, we study the case that there exist many Schur functions fulfilling the required conditions. For this situation, an application of the theory of orthogonal rational functions is used to characterize the set of all solutions of the problem in question. Moreover, we treat briefly the case of exactly one solution and present an explicit description of the unique solution in that case.

scholarly journals Orthogonal rational functions and modified approximants

1996 ◽  
Vol 11 (1) ◽  
pp. 57-69 ◽  
Author(s):  
A. Bultheel ◽  
P. González-Vera ◽  
E. Hendriksen ◽  
O. Njåstad
Keyword(s):  
Rational Functions ◽  
Orthogonal Rational Functions

scholarly journals Convergence of modified approximants associated with orthogonal rational functions

1995 ◽  
Vol 57 (1-2) ◽  
pp. 77-86 ◽  
Author(s):  
A. Bultheel ◽  
P. González-Vera ◽  
E. Hendriksen ◽  
O. Njåstad
Keyword(s):  
Rational Functions ◽  
Orthogonal Rational Functions
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