  A classical result due to Bochner characterizes the classical orthogonal
polynomial systems as solutions of a second-order eigenvalue equation. We
extend Bochner's result by dropping the assumption that the first element of
the orthogonal polynomial sequence be a constant. This approach gives rise to
new families of complete orthogonal polynomial systems that arise as solutions
of second-order eigenvalue equations with rational coefficients. The results
are based on a classification of exceptional polynomial subspaces of
codimension one under projective transformations.
