Analysis of Spectral Projectors in One-Dimensional Domains

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Abstract
In this paper we analyze a class of projection operators with values in a subspace of polynomials. These projection operators are related to the Hilbert spaces involved in the numerical analysis of spectral methods. They are, in the first part of the paper, the standard Sobolev spaces and, in the second part, some weighted Sobolev spaces, the weight of which is related to the orthogonality relation satisfied by the Chebyshev polynomials. These results are used to study the approximation of a model fourth-order problem.