Multivariate inequalities of Chernoff type for classical orthogonal polynomials
The authors present two-sided Chernoff-type inequalities for the error of the best approximation of a smooth \(d\)-variate function by polynomials of total degree less than \(k\) in the \(L^{2}_{w}\)-norm. The authors make the assumption that the \(d\)-variate weight function \(w\) has one-dimensional classical component weights, which satisfy Pearson differential equations.
multivariate classical orthogonal polynomials
scientific article; zbMATH DE number 6005673