scholarly journals ORTHOGONAL RATIONAL FUNCTIONS AND INTERPOLATORY PRODUCT RULES ON THE UNIT CIRCLE

Analysis ◽  
2000 ◽  
Vol 20 (2) ◽  
pp. 99-120 ◽  
Author(s):  
A. Bultheel ◽  
P. González-Vera ◽  
E. Hendriksen ◽  
O. Njåstad
Keyword(s):  
Unit Circle ◽  
Rational Functions ◽  
Orthogonal Rational Functions ◽  
Product Rules

scholarly journals Orthogonal rational functions and interpolatory product rules on the unit circle. II. Quadrature and convergence

Analysis ◽  
1998 ◽  
Vol 18 (2) ◽  
pp. 185-200 ◽  
Author(s):  
A. Bultheel ◽  
P. Gonzälez-Vera ◽  
Ε. Hendriksen ◽  
Ο. Njàstad
Keyword(s):  
Unit Circle ◽  
Rational Functions ◽  
Orthogonal Rational Functions ◽  
Product Rules

scholarly journals Orthogonal rational functions and interpolatory product rules on the unit circle. I. Recurrence and interpolation

Analysis ◽  
1998 ◽  
Vol 18 (2) ◽  
pp. 167-184 ◽  
Author(s):  
A. Bultheel ◽  
P. Gonzälez-Vera ◽  
E. Hendriksen ◽  
O. Njåstad
Keyword(s):  
Unit Circle ◽  
Rational Functions ◽  
Orthogonal Rational Functions ◽  
Product Rules

The Zero Distribution of Orthogonal Rational Functions on the Unit Circle

1997 ◽  
Vol 49 (4) ◽  
pp. 810-819
Author(s):  
K. Pan
Keyword(s):  
Unit Circle ◽  
Potential Theory ◽  
Rational Functions ◽  
Orthogonal Rational Functions ◽  
Zero Distribution

AbstractRational functions orthogonal on the unit circle with prescribed poles lying outside the unit circle are studied. We use the potential theory to discuss the zeros distribution for the orthogonal rational functions.

scholarly journals SCHUR–NEVANLINNA SEQUENCES OF RATIONAL FUNCTIONS

2007 ◽  
Vol 50 (3) ◽  
pp. 571-596 ◽  
Author(s):  
Adhemar Bultheel ◽  
Andreas Lasarow
Keyword(s):  
Unit Circle ◽  
Interpolation Problem ◽  
Schur Functions ◽  
Rational Functions ◽  
The Other ◽  
Complex Numbers ◽  
Orthogonal Rational Functions ◽  
All Solutions ◽  
The One

AbstractWe study certain sequences of rational functions with poles outside the unit circle. Such kinds of sequences are recursively constructed based on sequences of complex numbers with norm less than one. In fact, such sequences are closely related to the Schur–Nevanlinna algorithm for Schur functions on the one hand, and to orthogonal rational functions on the unit circle on the other. We shall see that rational functions belonging to a Schur–Nevanlinna sequence can be used to parametrize the set of all solutions of an interpolation problem of Nevanlinna–Pick type for Schur functions.

scholarly journals Orthogonal Rational Functions with Poles on the Unit Circle

1994 ◽  
Vol 182 (1) ◽  
pp. 221-243 ◽  
Author(s):  
A. Bultheel ◽  
P. Gonzalezvera ◽  
E. Hendriksen ◽  
O. Njastad
Keyword(s):  
Unit Circle ◽  
Rational Functions ◽  
Orthogonal Rational Functions

scholarly journals Orthogonal rational functions and quadrature on the unit circle

1992 ◽  
Vol 3 (1) ◽  
pp. 105-116 ◽  
Author(s):  
Adhemar Bultheel ◽  
Pablo González-Vera ◽  
Erik Hendriksen ◽  
Olav Njåstad
Keyword(s):  
Unit Circle ◽  
Rational Functions ◽  
Orthogonal Rational Functions
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