arXiv subjects

Bruno Eijsvoogel

Publications and source records attributed to Bruno Eijsvoogel.

3 recordsLinked to original sources

arXiv2022

$N\times N$ Matrix Time-/Band- Limiting examples

Time- and band-limiting in the context of orthogonal polynomials has been studied since the 1980's. It involves finding differential or difference operators with special commutative properties. More recently this topic has been generalized to the cases were the orthogonal polynomials are matrix-valued. Leading to differential or difference operators with matrix coefficients. So far the only explicit examples of such operators were $2\times 2$ matrices. In this paper we give a number of $N\times N$ examples and a counterexample to illustrate the role that strong Pearson equations can play in finding such examples.

math.CA↗

arXiv2021

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

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 related to certain difference operators acting on the matrix orthogonal polynomials. These operators belong to the so called Fourier algebras, which play a key role in the construction of the families. In order to illustrate duality, we describe a family of Charlier type matrix orthogonal polynomials with explicit shift operators which allow us to find explicit formulas for three term recurrences, difference operators and square norms. These are the essential ingredients for the construction of different dual families.

math.CA↗

arXiv2020

Ladder relations for a class of matrix valued orthogonal polynomials

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 $\mathbb{R}$, and we derive algebraic and differential relations for these MVOPs. A particular case of importance is that of MVOPs with respect to a matrix weight of the form $W(x)=e^{-v(x)}e^{xA} e^{xA^\ast}$ on the real line, where $v$ is a scalar polynomial of even degree with positive leading coefficient and $A$ is a constant matrix.

math.CA↗