Singular examples of the matrix Bochner problem

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Harmonic analysis on Euclidean spaces (42-XX) Approximations and expansions (41-XX)

Cites Work

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Matrix Gegenbauer polynomials: the \(2\times 2\) fundamental cases
Matrix valued orthogonal polynomials arising from the complex projective space
A sequence of matrix valued orthogonal polynomials associated to spherical functions
Matrix inner product having a matrix symmetric second-order differential operator
Matrix valued Jacobi polynomials
Matrix valued orthogonal polynomials of the Jacobi type
Matrix valued spherical functions associated to the complex projective plane
Matrix-valued Gegenbauer-type polynomials
A survey on orthogonal matrix polynomials satisfying second order differential equations
Über Sturm-Liouvillesche Polynomsysteme.
Matrix orthogonal polynomials whose derivatives are also orthogonal
The algebra of differential operators associated to a weight matrix
Matrix orthogonal polynomials satisfying second-order differential equations: coping without help from group representation theory
Some examples of orthogonal matrix polynomials satisfying odd order differential equations
Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory.
A matrix-valued solution to Bochner's problem
Second-Order Differential Operators Having Several Families of Orthogonal Matrix Polynomials as Eigenfunctions
The Algebra of Differential Operators for a Matrix Weight: An Ultraspherical Example
Matrix-Valued Orthogonal Polynomials Related to (SU(2)×SU(2), diag)
The matrix Bochner problem
The algebra of differential operators associated to a family of matrix-valued orthogonal polynomials: Five instructive examples
Fundamental aspects of the representation theory of Hermitian operators with deficiency index (𝑚,𝑚)

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