Darboux Transformations for Orthogonal Polynomials on the Real Line and on the Unit Circle

2021 ◽  
pp. 53-75
Author(s):  
María José Cantero ◽  
Francisco Marcellán ◽  
Leandro Moral ◽  
Luis Velázquez
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Real Line ◽  
Darboux Transformations ◽  
The Real

scholarly journals New Stability Criteria for Discrete Linear Systems Based on Orthogonal Polynomials

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1322
Author(s):  
Luis E. Garza ◽  
Noé Martínez ◽  
Gerardo Romero
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Linear Systems ◽  
Real Line ◽  
Stability Criteria ◽  
The Real ◽  
Discrete Linear Systems ◽  
New Criterion ◽  
Schur Stability

A new criterion for Schur stability is derived by using basic results of the theory of orthogonal polynomials. In particular, we use the relation between orthogonal polynomials on the real line and on the unit circle known as the Szegő transformation. Some examples are presented.

scholarly journals A CMV connection between orthogonal polynomials on the unit circle and the real line

2021 ◽  
pp. 105579
Author(s):  
M.J. Cantero ◽  
F. Marcellán ◽  
L. Moral ◽  
L. Velázquez
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Real Line ◽  
The Real

On perturbed orthogonal polynomials on the real line and the unit circle via Szegő’s transformation

2017 ◽  
Vol 302 ◽  
pp. 97-110 ◽  
Author(s):  
Kenier Castillo ◽  
Francisco Marcellán ◽  
Jorge Rivero
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Real Line ◽  
The Real

scholarly journals Sylvester equations for Laguerre–Hahn orthogonal polynomials on the real line

2013 ◽  
Vol 219 (17) ◽  
pp. 9118-9131 ◽  
Author(s):  
A. Branquinho ◽  
A. Paiva ◽  
M.N. Rebocho
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
The Real

scholarly journals LOWERING AND RAISING OPERATORS FOR THE FREE MEIXNER CLASS OF ORTHOGONAL POLYNOMIALS

2009 ◽  
Vol 12 (03) ◽  
pp. 387-399 ◽  
Author(s):  
EUGENE LYTVYNOV ◽  
IRINA RODIONOVA
Keyword(s):  
Orthogonal Polynomials ◽  
Real Line ◽  
Meixner Polynomials ◽  
The Real ◽  
Raising Operators ◽  
Meixner Class

We compare some properties of the lowering and raising operators for the classical and free classes of Meixner polynomials on the real line.

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