Unbounded commuting operators and multivariate orthogonal polynomials

Xu, Yuan

doi:10.1090/S0002-9939-1993-1165065-7

Unbounded commuting operators and multivariate orthogonal polynomials
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Proc. Amer. Math. Soc. 119 (1993), 1223-1231 Request permission

Abstract:

The multivariate orthogonal polynomials are related to a family of operators whose matrix representations are block Jacobi matrices. A sufficient condition is given so that these operators, in general unbounded, are commuting and selfadjoint. The spectral theorem for these operators is used to establish the existence of the measure of orthogonality in Favard’s theorem.

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