scholarly journals Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials

2016 ◽  
Vol 28 (1) ◽  
pp. 74-90 ◽  
Author(s):  
A. Branquinho ◽  
A. Foulquié Moreno ◽  
A. Mendes
Keyword(s):  
Orthogonal Polynomials ◽  
Integrable Systems ◽  
Matrix Orthogonal Polynomials

scholarly journals About several classes of bi-orthogonal polynomials and discrete integrable systems

2014 ◽  
Vol 48 (1) ◽  
pp. 015204 ◽  
Author(s):  
Xiang-Ke Chang ◽  
Xiao-Min Chen ◽  
Xing-Biao Hu ◽  
Hon-Wah Tam
Keyword(s):  
Orthogonal Polynomials ◽  
Integrable Systems ◽  
Discrete Integrable Systems

Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions

Nonlinearity ◽  
2015 ◽  
Vol 28 (7) ◽  
pp. 2279-2306 ◽  
Author(s):  
Xiao-Min Chen ◽  
Xiang-Ke Chang ◽  
Jian-Qing Sun ◽  
Xing-Biao Hu ◽  
Yeong-Nan Yeh
Keyword(s):  
Orthogonal Polynomials ◽  
Integrable Systems ◽  
Discrete Integrable Systems

scholarly journals On the Christoffel–Darboux formula for generalized matrix orthogonal polynomials

2014 ◽  
Vol 418 (1) ◽  
pp. 238-247 ◽  
Author(s):  
Carlos Álvarez-Fernández ◽  
Manuel Mañas
Keyword(s):  
Orthogonal Polynomials ◽  
Matrix Orthogonal Polynomials ◽  
Generalized Matrix

Time-and-band limiting for matrix orthogonal polynomials of Jacobi type

2017 ◽  
Vol 06 (04) ◽  
pp. 1740001 ◽  
Author(s):  
M. Castro ◽  
F. A. Grünbaum
Keyword(s):  
Signal Processing ◽  
Differential Operator ◽  
Orthogonal Polynomials ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Jacobi Polynomials ◽  
Matrix Theory ◽  
Matrix Orthogonal Polynomials

We extend to a situation involving matrix-valued orthogonal polynomials a scalar result that plays an important role in Random Matrix Theory and a few other areas of mathe-matics and signal processing. We consider a case of matrix-valued Jacobi polynomials which arises from the study of representations of [Formula: see text], a group that plays an important role in Random Matrix Theory. We show that in this case an algebraic miracle, namely the existence of a differential operator that commutes with a naturally arising integral one, extends to this matrix-valued situation.

scholarly journals The Darboux process and time-and-band limiting for matrix orthogonal polynomials

2015 ◽  
Vol 487 ◽  
pp. 328-341 ◽  
Author(s):  
M. Castro ◽  
F.A. Grünbaum
Keyword(s):  
Orthogonal Polynomials ◽  
Matrix Orthogonal Polynomials

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

2003 ◽  
Vol 154 (2) ◽  
pp. 247-272 ◽  
Author(s):  
M.J Cantero ◽  
M.P Ferrer ◽  
L Moral ◽  
L Velázquez
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Real Line ◽  
The Real ◽  
Matrix Orthogonal Polynomials

scholarly journals Bi-orthogonal Polynomials on the Unit Circle, Regular Semi-Classical Weights and Integrable Systems

2006 ◽  
Vol 24 (2) ◽  
pp. 201-237 ◽  
Author(s):  
P.J. Forrester ◽  
N.S. Witte
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Integrable Systems
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