Multivariate Stieltjes type theorems and location of common zeros of multivariate orthogonal polynomials. (English summary) J. Math. Anal. Appl. 336 (2007), no. 1, 127–139. For orthogonal polynomials of d real variables the authors introduce a notion of invariant factors (d ∈ N). Some properties of the invariant factors are established. In particular, these factors are one-variable polynomials, their roots are real and they are eigenvalues of the Jacobi matrix corresponding to the orthogonal polynomials. A theorem of Stieltjes type is established. Using properties of the invariant factors some properties of the common zeros of the orthogonal polynomials (in particular, their location) are obtained. The results are illustrated by two examples o
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