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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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