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We analyze the approximation properties of some interpolation operators and some L ω 2 L_ ² -orthogonal projection operators related to systems of polynomials which are orthonormal with respect to a weight function ω (x 1, …, x d) (x₁, , xd), d ⩾ 1 d 1. The error estimates for the Legendre system and the Chebyshev system of the first kind are given in the norms of the Sobolev spaces H ω s H_ ˢ. These results are useful in the numerical analysis of the approximation of partial differential equations by spectral methods.
Canuto et al. (Fri,) studied this question.