On some Sobolev spaces with matrix weights and classical type Sobolev orthogonal polynomials

For every system {p(n)(z)}(n=0)(infinity) of OPRL or OPUC, we construct Sobolev orthogonal polynomials y(n)(z), with explicit integral representations involving p(n). Two concrete families of Sobolev orthogonal polynomials (depending on an arbitrary number of complex parameters) which are generalized eigenvalues of a difference operator (in n) and generalized eigenvalues of a differential operator (in z) are given. We define suitable Sobolev spaces with matrix weights and consider measurable factorizations of weights. Applications of a general connection between Sobolev orthogonal polynomials and orthogonal systems of functions in the direct sum of scalar L-mu(2) spaces are discussed.