Multivariate Orthogonal Polynomials and Operator Theory

DOI10.2307/2154528zbMath0832.42017OpenAlexW2007681366MaRDI QIDQ4300930

Yuan Xu

Publication date: 6 February 1996

Full work available at URL: https://doi.org/10.2307/2154528

zbMATH Keywords

spectral theorythree-term recurrence relationsmultivariate orthogonal polynomialscommuting selfadjoint operators

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15)

Related Items

Multivariate orthogonal Laurent polynomials and integrable systems ⋮ Multivariate Toda hierarchies and biorthogonal polynomials ⋮ Multivariate orthogonal polynomials and integrable systems ⋮ Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains ⋮ Tridiagonal operators and zeros of polynomials in two variables ⋮ Christoffel-Darboux kernels in several real variables ⋮ A Stieltjes Algorithm for Generating Multivariate Orthogonal Polynomials ⋮ Linear partial \(q\)-difference equations on \(q\)-linear lattices and their bivariate \(q\)-orthogonal polynomial solutions ⋮ Bivariate Symmetric Discrete Orthogonal Polynomials ⋮ Bivariate second-order linear partial differential equations and orthogonal polynomial solutions ⋮ On a class of bivariate second-order linear partial difference equations and their monic orthogonal polynomial solutions ⋮ Commuting family of block Jacobi matrices ⋮ Recurrence Formulas for Multivariate Orthogonal Polynomials ⋮ Block Jacobi Matrices and Zeros of Multivariate Orthogonal Polynomials ⋮ Unbounded Commuting Operators and Multivariate Orthogonal Polynomials ⋮ Three term recurrence relation modulo ideal and orthogonality of polynomials of several variables ⋮ Solutions of Three-Term Relations in Several Variables ⋮ On Bivariate Gaussian Cubature Formulae ⋮ Multivariate orthogonal polynomials: quantum decomposition, deficiency rank and support of measure

Cites Work

• Tridiagonal matrix representations of cyclic self-adjoint operators
• Analytic vectors
• The multidimensional moment problem
• Multiparameter spectral theory in Hilbert space
• Orthogonal polynomials in two variables
• Orthogonality and Recursion Formulas for Polynomials in n Variables
• Note on Orthogonal Polynomials inv-Variables
• On Multivariate Orthogonal Polynomials
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item