Soit un espace de Banach et la boule de rayon centrée en 0. 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 pour une certaine classe d’espaces, en particulier pour la plupart des espaces de Banach classiques.
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.
@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}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {50}, number = {2}, year = {2000}, doi = {10.5802/aif.1760}, mrnumber = {2001g:32052}, zbl = {0969.46032}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1760/} }
TY - JOUR AU - Lempert, László TI - Approximation of holomorphic functions of infinitely many variables II JO - Annales de l'Institut Fourier PY - 2000 SP - 423 EP - 442 VL - 50 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1760/ DO - 10.5802/aif.1760 LA - en ID - AIF_2000__50_2_423_0 ER -
%0 Journal Article %A Lempert, László %T Approximation of holomorphic functions of infinitely many variables II %J Annales de l'Institut Fourier %D 2000 %P 423-442 %V 50 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1760/ %R 10.5802/aif.1760 %G en %F AIF_2000__50_2_423_0
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. http://archive.numdam.org/articles/10.5802/aif.1760/
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