Multiple Orthogonal Polynomials on the Unit Circle

2007 ◽  
Vol 28 (2) ◽  
pp. 173-197 ◽  
Author(s):  
Judit Minguez Ceniceros ◽  
Walter Van Assche
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Multiple Orthogonal Polynomials

scholarly journals Strong asymptotics for the Pollaczek multiple orthogonal polynomials

2015 ◽  
Vol 92 (3) ◽  
pp. 709-713
Author(s):  
A. I. Aptekarev ◽  
G. López Lagomasino ◽  
A. Martínez-Finkelshtein
Keyword(s):  
Orthogonal Polynomials ◽  
Strong Asymptotics ◽  
Multiple Orthogonal Polynomials

Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle

2013 ◽  
Vol 286 (17-18) ◽  
pp. 1778-1791 ◽  
Author(s):  
Dimitar K. Dimitrov ◽  
A. Sri Ranga
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle

scholarly journals THE GENERALIZED MATRIX VALUED HYPERGEOMETRIC EQUATION

2010 ◽  
Vol 21 (02) ◽  
pp. 145-155 ◽  
Author(s):  
P. ROMÁN ◽  
S. SIMONDI
Keyword(s):  
Differential Equation ◽  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Hypergeometric Functions ◽  
Spherical Functions ◽  
Hypergeometric Equation ◽  
Necessary Condition ◽  
Hypergeometric Differential Equation ◽  
The Matrix ◽  
Generalized Matrix

The matrix valued analog of the Euler's hypergeometric differential equation was introduced by Tirao in [4]. This equation arises in the study of matrix valued spherical functions and in the theory of matrix valued orthogonal polynomials. The goal of this paper is to extend naturally the number of parameters of Tirao's equation in order to get a generalized matrix valued hypergeometric equation. We take advantage of the tools and strategies developed in [4] to identify the corresponding matrix hypergeometric functions nFm. We prove that, if n = m + 1, these functions are analytic for |z| < 1 and we give a necessary condition for the convergence on the unit circle |z| = 1.

Sign in / Sign up

Export Citation Format

Share Document