Unbounded Commuting Operators and Multivariate Orthogonal Polynomials
نویسندگان
چکیده
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.
منابع مشابه
Multivariate Orthogonal Polynomials and Operator Theory
The multivariate orthogonal polynomials are related to a family of commuting selfadjoint operators. The spectral theorem for these operators is used to prove that a polynomial sequence satisfying a vector-matrix form of the three-term relation is orthonormal with a determinate measure.
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