Approximation by finite element functions using local regularization
General Besov and Triebel-Lizorkin spaces on domains with irregular boundary are compared with the completion, in those spaces, of the subset of infinitely continuously differentiable functions with compact support in the same domains. It turns out that the set of parameters for which those spaces coincide is strongly related to the fractal dimension of the boundary of the domains.
Let G be a locally compact Hausdorff group with Haar measure, and let L⁰(G) be the space of extended real-valued measurable functions on G, finite a.e. Let ϱ and η be modulars on L⁰(G). The error of approximation ϱ(a(Tf - f)) of a function is estimated, where and K satisfies a generalized Lipschitz condition with respect to the second variable.
We investigate the approximation properties of the partial sums of the Fourier series and prove some direct and inverse theorems for approximation by polynomials in weighted Orlicz spaces. In particular we obtain a constructive characterization of the generalized Lipschitz classes in these spaces.
Soit un compact de de la forme où chaque est soit l’adhérence d’un domaine strictement pseudoconvexe dans , soit l’adhérence d’un polyèdre de Weil régulier, ou encore un compact de . étant un espace de Fréchet, on montre que lorsque appartient à avec alors est approchable uniformément sur par des fonctions holomorphes au voisinage de et à valeurs dans . On donne également des résultats de localisation pour l’espace .
Soit un espace de Banach complexe, et notons la boule de rayon centrée en . On considère le problème d’approximation suivant: étant donnés , et une fonction holomorphe dans , existe-t-il toujours une fonction , holomorphe dans , telle que sur ? On démontre que c’est bien le cas si est l’espace des suites sommables.
Let be a complex Banach space. Recall that admits afinite-dimensional Schauder decompositionif there exists a sequence of finite-dimensional subspaces of such that every has a unique representation of the form with for every The finite-dimensional Schauder decomposition is said to beunconditionalif, for every the series which represents converges unconditionally, that is, converges for every permutation of the integers. For short, we say that admits an unconditional F.D.D.We...
Let be a Banach space and the ball of radius centered at . Can any holomorphic function on be approximated by entire functions, uniformly on smaller balls ? We answer this question in the affirmative for a large class of Banach spaces.
In this article we examine necessary and sufficient conditions for the predual of the space of holomorphic mappings of bounded type, Gb(U), to have the approximation property and the compact approximation property and we consider when the predual of the space of holomorphic mappings, G(U), has the compact approximation property. We obtain also similar results for the preduals of spaces of m-homogeneous polynomials, Q(mE).