Orthogonal polynomials satisfying fourth order differential equations were classified by HL
Krall [K2]. They can be obtained from very special instances of the (generalized) Laguerre …

General methods for constructing bispectral operators Page 1 21 October 1996 Physics Letters
A 222 (1996) 59-66 PHYSICS LETTERS A General methods for constructing bispectral …

We study a certain family of Schrödinger operators whose eigenfunctions ϕ (χ, λ) satisfy a
differential equation in the spectral parameter λ of the form B (λ,∂ λ) ϕ= Θ (x) ϕ. We show …

We develop a systematic way for constructing bispectral algebras of commuting ordinary
differential operators of any rank N. It combines and unifies the ideas of Duistermaat …

Consider a fixed family of orthogonal matrix polynomials P n that are common
eigenfunctions of some differential operator L with matrix coefficients and a matrix-valued …

This paper considers Darboux transformations of a bispectral operator which preserve its
bispectrality. A sufficient condition for this to occur is given, and applied to the case of …

Classical prolate spheroidal functions play an important role in the study of time-band
limiting, scaling limits of random matrices, and the distribution of the zeros of the Riemann …

Pairs of n× n matrices whose commutator differ from the identity by a matrix of rank r are
used to construct bispectral differential operators with r× r matrix coefficients satisfying the …

We consider the fundamental solutions of a wide class of first order systems with polynomial
dependence on the spectral parameter and rational matrix potentials. Such matrix potentials …

We consider a matrix valued version of the bispectral problem involving a block tridiagonal
doubly infinite matrix and a first-order differential operator with matrix coefficients. We give a …