Approximation of holomorphic functions of infinitely many variables II

Lempert, László

doi:10.5802/aif.1760

Lempert, László

Annales de l'Institut Fourier, Tome 50 (2000) no. 2, pp. 423-442.

Résumé
Abstract

Soit $X$ un espace de Banach et $B (R) \subset X$ la boule de rayon $R$ centrée en 0. Étant donnés $0 < r < R, ε > 0$ et une fonction $f$ holomorphe dans $B (R)$ , existe-t-il toujours une fonction $g$ , holomorphe dans $X$ , telle que $| f - g | < ε$ sur $B (r)$ ? On démontre que c’est bien le cas pour une certaine classe d’espaces, en particulier pour la plupart des espaces de Banach classiques.

Let $X$ be a Banach space and $B (R) \subset X$ the ball of radius $R$ centered at $0$ . Can any holomorphic function on $B (R)$ be approximated by entire functions, uniformly on smaller balls $B (r)$ ? We answer this question in the affirmative for a large class of Banach spaces.

MR Zbl | 4 citations dans Numdam

DOI : 10.5802/aif.1760

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Lempert, László. Approximation of holomorphic functions of infinitely many variables II. Annales de l'Institut Fourier, Tome 50 (2000) no. 2, pp. 423-442. doi : 10.5802/aif.1760. https://www.numdam.org/articles/10.5802/aif.1760/

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