no. 2
Approximation of holomorphic functions of infinitely many variables II
Annales de l'Institut Fourier, Tome 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.

@article{AIF_2000__50_2_423_0,
     author = {Lempert, L\'aszl\'o},
     title = {Approximation of holomorphic functions of infinitely many variables {II}},
     journal = {Annales de l'Institut Fourier},
     pages = {423--442},
     year = {2000},
     publisher = {Association des Annales de l'Institut Fourier},
     volume = {50},
     number = {2},
     doi = {10.5802/aif.1760},
     mrnumber = {2001g:32052},
     zbl = {0969.46032},
     language = {en},
     url = {https://www.numdam.org/articles/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

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