Properties of Multivariate Homogeneous Orthogonal Polynomials

It is well-known that the denominators of Pade approximants can be considered as orthogonal polynomials with respect to a linear functional. This is usually shown by defining Pade -type approximants from so-called generating polynomials and then improving the order of approximation by imposing orthogonality conditions on the generating polynomials. In the multivariate case, a similar construction is possible when dealing with the multivariate homogeneous Pade approximants introduced by the second author. Moreover it is shown here, that several well-known properties of the zeroes of classical univariate orthogonal polynomials, in the case of a definite linear functional, generalize to the multivariate homogeneous case. For the multivariate homogeneous orthogonal polynomials, the absence of common zeroes is translated to the absence of common factors. 2001 Academic Press