Multi-variable orthogonal polynomials

2014/01/21 by Dhahri, Abdallah
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1401.5434

Abstract

We characterize the atomic probability measure on ℝ^d which having a finite number of atoms. We further prove that the Jacobi sequences associated to the multiple Hermite (resp. Laguerre, resp. Jacobi) orthogonal polynomials are diagonal matrices. Finally, as a consequence of the multiple Jacobi orthogonal polynomials case, we give the Jacobi sequences of the Gegenbauer, Chebyshev and Legendre orthogonal polynomials.

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