Christoffel Functions and Fourier Series for Multivariate Orthogonal Polynomials Original Research Article

The Christoffel functions Λn(dμ) associated with a general nonnegative measure μ on Rd are studied. The asymptotics of Λn(dμ) are derived for μ supported on [− 1,1]d. The estimates of Λn(dμ) are used to study the summability of the multivariate orthogonal polynomials associated with μ. The pointwise convergence of the partial sums of the orthogonal expansion, and their (C, 1) and de la Vallée Poussin means are considered.