scholarly journals Coherent pairs of bivariate orthogonal polynomials

2019 ◽  
Vol 245 ◽  
pp. 40-63 ◽  
Author(s):  
Francisco Marcellán ◽  
Misael E. Marriaga ◽  
Teresa E. Pérez ◽  
Miguel A. Piñar
Keyword(s):  
Orthogonal Polynomials ◽  
Coherent Pairs

scholarly journals Asymptotics for Jacobi–Sobolev orthogonal polynomials associated with non-coherent pairs of measures

2010 ◽  
Vol 162 (11) ◽  
pp. 1945-1963 ◽  
Author(s):  
Eliana X.L. de Andrade ◽  
Cleonice F. Bracciali ◽  
Laura Castaño-García ◽  
Juan J. Moreno-Balcázar
Keyword(s):  
Orthogonal Polynomials ◽  
Sobolev Orthogonal Polynomials ◽  
Coherent Pairs

Asymptotics of Sobolev orthogonal polynomials for Hermite (1,1)-coherent pairs

2018 ◽  
Vol 467 (1) ◽  
pp. 601-621 ◽  
Author(s):  
Herbert Dueñas Ruiz ◽  
Francisco Marcellán Español ◽  
Alejandro Molano Molano
Keyword(s):  
Orthogonal Polynomials ◽  
Sobolev Orthogonal Polynomials ◽  
Coherent Pairs

scholarly journals (1,1)-Coherent Pairs on the Unit Circle

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Luis Garza ◽  
Francisco Marcellán ◽  
Natalia C. Pinzón-Cortés
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Linear Functional ◽  
Linear Functionals ◽  
Spectral Transformation ◽  
Coherent Pair ◽  
Coherent Pairs

A pair(𝒰,𝒱)of Hermitian regular linear functionals on the unit circle is said to be a(1,1)-coherent pair if their corresponding sequences of monic orthogonal polynomials{ϕn(x)}n≥0and{ψn(x)}n≥0satisfyϕn[1](z)+anϕn-1[1](z)=ψn(z)+bnψn-1(z),an≠0,n≥1, whereϕn[1](z)=ϕn+1′(z)/(n+1). In this contribution, we consider the cases when𝒰is the linear functional associated with the Lebesgue and Bernstein-Szegő measures, respectively, and we obtain a classification of the situations where𝒱is associated with either a positive nontrivial measure or its rational spectral transformation.

scholarly journals q-Coherent pairs and q-orthogonal polynomials

2002 ◽  
Vol 128 (2-3) ◽  
pp. 191-216 ◽  
Author(s):  
I. Area ◽  
E. Godoy ◽  
F. Marcellán
Keyword(s):  
Orthogonal Polynomials ◽  
Coherent Pairs
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