Sobolev orthogonal polynomials and spectral differential equations

We find necessary and sufficient conditions for a spectral differential equation N LN(y)(x) = 52ti(x)yW(x) = kny(x) (-1 to have Sobolev orthogonal polynomials of solutions, which are orthogonal rel- ative to the Sobolev (pseudo-) inner product c t (P ,q)= / Pqdn + I p'q'du,