Symmetrizability of differential equations having orthogonal polynomial solutions

Abstract

We show that if a linear differential equation of spectral type with polynomial coefficients L-N[y](x) = (i=0)Sigma(N)l(i)(x)y((i))(x)=lambda(n)y(x) has an orthogonal polynomial system of solutions, then the differential operator L-N[.] must be symmetrizable. We also give a few applications of this result.