Connections between Interval and Unit Circle for Sobolev Orthogonal Polynomials. Strong Asymptotics on the Real Line

2005 ◽  
Vol 86 (3) ◽  
pp. 221-236 ◽  
Author(s):  
E. Berriochoa ◽  
A. Cachafeiro ◽  
J. Garc�a-Amor
Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1322
Author(s):  
Luis E. Garza ◽  
Noé Martínez ◽  
Gerardo Romero

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.


2021 ◽  
pp. 105579
Author(s):  
M.J. Cantero ◽  
F. Marcellán ◽  
L. Moral ◽  
L. Velázquez

2019 ◽  
Vol 53 (2) ◽  
pp. 139-164
Author(s):  
Herbert Dueñas Ruiz ◽  
Francisco Marcellán ◽  
Alejandro Molano

In the pioneering paper [13], the concept of Coherent Pair was introduced by Iserles et al. In particular, an algorithm to compute Fourier Coefficients in expansions of Sobolev orthogonal polynomials defined from coherent pairs of measures supported on an infinite subset of the real line is described. In this paper we extend such an algorithm in the framework of the so called Symmetric (1, 1)-Coherent Pairs presented in [8].


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