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Approximation de fonctions holomorphes d'un nombre infini de variables

László Lempert (1999)

Annales de l'institut Fourier

Soit X un espace de Banach complexe, et notons B ( R ) X la boule de rayon R centrée en 0 . On considère le problème d’approximation suivant: 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 si X est l’espace l 1 des suites sommables.

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