# Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda lattice

@article{Ismail2018MatrixVH, title={Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda lattice}, author={Mourad E. H. Ismail and Erik Koelink and Pablo Rom{\'a}n}, journal={Adv. Appl. Math.}, year={2018}, volume={110}, pages={235-269} }

## 15 Citations

### Matrix Orthogonal Polynomials, non-abelian Toda lattice and B\"acklund transformation

- Mathematics
- 2021

Abstract. A connection between matrix orthogonal polynomials and non-abelian integrable lattices is investigated in this paper. The normalization factors of matrix orthogonal polynomials expressed by…

### Duality and difference operators for matrix valued discrete polynomials on the nonnegative integers

- Mathematics
- 2021

In this paper we introduce a notion of duality for matrix valued orthogonal polynomials with respect to a measure supported on the nonnegative integers. We show that the dual families are closely…

### Matrix Valued Laguerre Polynomials

- MathematicsTrends in Mathematics
- 2019

Matrix valued Laguerre polynomials are introduced via a matrix weight function involving several degrees of freedom using the matrix nature. Under suitable conditions on the parameters the matrix…

### Matrix-Valued hypergeometric Appell-Type polynomials

- MathematicsElectronic Research Archive
- 2022

In recent years, much attention has been paid to the role of special matrix polynomials of a real or complex variable in mathematical physics, especially in boundary value problems. In this article,…

### Matrix orthogonality in the plane versus scalar orthogonality in a Riemann surface

- Mathematics, Computer ScienceTransactions of Mathematics and Its Applications
- 2021

It is shown that the Christoffel–Darboux (CD) kernel, which is built in terms of matrix orthogonal polynomials, is equivalent to a scalar valued reproducing kernel of meromorphic functions in a Riemann surface.

### Ladder relations for a class of matrix valued orthogonal polynomials

- MathematicsStudies in Applied Mathematics
- 2020

Using the theory introduced by Casper and Yakimov, we investigate the structure of algebras of differential and difference operators acting on matrix valued orthogonal polynomials (MVOPs) on R , and…

### Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

- MathematicsAdvances in Difference Equations
- 2021

Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels, in this article we derive…

### Recursion and Hamiltonian operators for integrable nonabelian difference equations

- MathematicsNonlinearity
- 2020

In this paper, we carry out the algebraic study of integrable differential-difference equations whose field variables take values in an associative (but not commutative) algebra. We adapt the…

### On Fourier–Bessel matrix transforms and applications

- MathematicsMathematical Methods in the Applied Sciences
- 2021

The Fourier–Bessel transform is an integral transform and is also known as the Hankel transform. This transform is a very important tool in solving many problems in mathematical sciences, physics,…

### Orthogonal functions related to Lax pairs in Lie algebras

- Mathematics
- 2020

We study a Lax pair in a $2$-parameter Lie algebra in various representations. The overlap coefficients of the eigenfunctions of $L$ and the standard basis are given in terms of orthogonal…

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