Vector orthogonal polynomials

摘要

The following well-known framework will be applied to Hermite-Padé approximants. First the Hermite-Padé-type approximants will be defined. From the error of approximation some supplementary conditions will be fixed in order to obtain Hermite-Padé-forms. Vector orthogonal polynomials will be deduced from these conditions. Their existence and uniqueness are studied. In the normal case these results are ensured. Then some properties of vector orthogonal polynomials will be proved.