Estimations des erreurs de meilleure approximation polynomiale et d'interpolation de Lagrange dans les espaces de Sobolev d'ordre non entier

Abstract

R6sum6. On 6tablit des majorations explicites de l'erreur de meilleure approximation polynomiale ainsi que des majorations explicites et nonexplicites de l'erreur d'interpolation de Lagrange, lorsque la fonction consid6r6e appartient /tun espace de Sobolev d'ordre non entier d6fini sur un ouvert born6 de ~".Les r6sultats obtenus g6ndralisent les r6sultats connus dans le cas des espaces de Sobolev d'ordre entier. Summary.Explicit bounds for the best polynomial approximation error, explicit and non-explicit bounds for the Lagrange interpolation error are derived for functions belonging to fractional order Sobolev spaces defined over a bounded open set in F,.".Thus the classical results of the integer order Sobolev spaces are extended.

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