scholarly journals Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonal polynomials

2002 ◽  
Vol 18 (3) ◽  
pp. 923-942 ◽  
Author(s):  
J Coussement ◽  
A B J Kuijlaars ◽  
W Van Assche
Keyword(s):  
Orthogonal Polynomials ◽  
Toda Lattice ◽  
Spectral Transform ◽  
Inverse Spectral ◽  
Relativistic Toda Lattice

scholarly journals Extended Relativistic Toda Lattice, L-Orthogonal Polynomials and Associated Lax Pair

2018 ◽  
Vol 164 (1) ◽  
pp. 137-154
Author(s):  
Cleonice F. Bracciali ◽  
Jairo S. Silva ◽  
A. Sri Ranga
Keyword(s):  
Orthogonal Polynomials ◽  
Toda Lattice ◽  
Lax Pair ◽  
Relativistic Toda Lattice

scholarly journals Orthogonal polynomials associated with an inverse spectral transform. The cubic case

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2477-2497
Author(s):  
Mabrouk Sghaier ◽  
Lamaa Khaled
Keyword(s):  
Orthogonal Polynomials ◽  
Monic Polynomial ◽  
Polynomial Sequence ◽  
Spectral Transform ◽  
Algebraic Properties ◽  
Inverse Spectral

The purpose of this work is to give some new algebraic properties of the orthogonality of a monic polynomial sequence {Qn}n ? o defined by Qn(X) = Pn(X) + SnPn-1(X) + tnPn-2(X) + rnPn-3(X), n ? 1, where rn ? 0, n ? 3, and {Pn}n?0 is a given sequence of monic orthogonal polynomials. Essentially, we consider some cases in which the parameters rn, sn, and tn can be computed more easily. Also, as a consequence, a matrix interpretation using LU and UL factorization is done. Some applications for Laguerre, Bessel and Tchebychev orthogonal polynomials of second kind are obtained.

scholarly journals A q-generalization of the Toda equations for the q-Laguerre/Hermite orthogonal polynomials

2018 ◽  
Vol 07 (04) ◽  
pp. 1840002 ◽  
Author(s):  
Chuan-Tsung Chan ◽  
Hsiao-Fan Liu
Keyword(s):  
Orthogonal Polynomials ◽  
Deformation Theory ◽  
Toda Lattice ◽  
Quadratic Relation ◽  
Lax Equation ◽  
Toda Equations

Based on the motivation of generalizing the correspondence between the Lax equation for the Toda lattice and the deformation theory of the orthogonal polynomials, we derive a [Formula: see text]-deformed version of the Toda equations for both [Formula: see text]-Laguerre/Hermite ensembles, and check the compatibility with the quadratic relation.

The Klein-Gordon inverse spectral transform

1980 ◽  
Vol 28 (3) ◽  
pp. 107-111 ◽  
Author(s):  
J. J. P. Leon
Keyword(s):  
Spectral Transform ◽  
Klein Gordon ◽  
Inverse Spectral
Sign in / Sign up

Export Citation Format

Share Document