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Approximation results for orthogonal polynomials in Sobolev spaces. (English) Zbl 0567.41008
We analyze the approximation properties of some interpolation operators and some $$L^ 2_{\omega}$$-orthogonal projection operators related to systems of polynomials which are orthonormal with respect to a weight function $$\omega (x_ 1,...,x_ d)$$, $$d\geq 1$$. The error estimates for the Legendre system and the Chebyshev system of the first kind are given in the norms of the Sobolev spaces $$H^ s_{\omega}$$. These results are useful in the numerical analysis of the approximation of partial differential equations by spectral methods.

##### MSC:
 41A10 Approximation by polynomials 41A05 Interpolation in approximation theory
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