no. 2
Approximation of holomorphic functions of infinitely many variables II
Annales de l'Institut Fourier, Volume 50 (2000) no. 2, pp. 423-442

Let X be a Banach space and B(R)⊂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.

Soit X un espace de Banach et B(R)⊂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.

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