Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second order differential operators having several families of
  orthogonal matrix polynomials as eigenfunctions   The aim of this paper is to bring into the picture a new phenomenon in the
theory of orthogonal matrix polynomials satisfying second order differential
equations. The last few years have witnessed some examples of a (fixed) family
of orthogonal matrix polynomials whose elements are common eigenfunctions of
several linearly independent second order differential operators. We show that
the dual situation is also possible: there are examples of different families
of matrix polynomials, each family orthogonal with respect to a different
weight matrix, whose elements are eigenfunctions of a common second order
differential operator.
  These examples are constructed by adding a discrete mass at certain point to
a weight matrix: $\widetilde{W}=W+\delta_{t_0}M(t_0)$. Our method consists in
showing how to choose the discrete mass $M(t_0)$, the point $t_0$ where the
mass lives and the weight matrix $W$ so that the new weight matrix
$\widetilde{W}$ inherits some of the symmetric second order differential
operators associated with $W$. It is well known that this situation is not
possible for the classical scalar families of Hermite, Laguerre and Jacobi.

12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys