Abstract
Polynomial perturbations of real multivariate measures are discussed and corresponding Christoffel type formulas are found. The 1D Christoffel formula is extended to the multidimensional realm: multivariate orthogonal polynomials are expressed in terms of last quasi-determinants and sample matrices. The coefficients of these matrices are the original orthogonal polynomials evaluated at a set of nodes, which is supposed to be poised. A discussion for the existence of poised sets is given in terms of algebraic hypersurfaces in the complex affine space. Two examples of irreducible perturbations of total degree 1 and 2, for the bivariate product Legendre orthogonal polynomials, are discussed in detail.
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