scholarly journals Multivariate orthogonal polynomials: Quantum decomposition, deficiency rank and support of measure

2020 ◽  
Vol 485 (1) ◽  
pp. 123775
Author(s):  
Ameur Dhahri ◽  
Nobuaki Obata ◽  
Hyun Jae Yoo
Keyword(s):  
Orthogonal Polynomials ◽  
Multivariate Orthogonal Polynomials

Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials

2013 ◽  
Vol 65 (3) ◽  
pp. 600-620 ◽  
Author(s):  
A. Kroó ◽  
D. S. Lubinsky
Keyword(s):  
Orthogonal Polynomials ◽  
Compact Set ◽  
Christoffel Functions ◽  
Analytic Parametrization ◽  
Multivariate Orthogonal Polynomials ◽  
General Conditions

AbstractWe establish asymptotics for Christoffel functions associated with multivariate orthogonal polynomials. The underlying measures are assumed to be regular on a suitable domain. In particular, this is true if they are positive a.e. on a compact set that admits analytic parametrization. As a consequence, we obtain asymptotics for Christoffel functions for measures on the ball and simplex under far more general conditions than previously known. As another consequence, we establish universality type limits in the bulk in a variety of settings.

scholarly journals A semiclassical perspective on multivariate orthogonal polynomials

2008 ◽  
Vol 214 (2) ◽  
pp. 447-456 ◽  
Author(s):  
María Álvarez de Morales ◽  
Lidia Fernández ◽  
Teresa E. Pérez ◽  
Miguel A. Piñar
Keyword(s):  
Orthogonal Polynomials ◽  
Multivariate Orthogonal Polynomials
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