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Analytic cohomology of complete intersections in a Banach space

Imre Patyi (2004)

Annales de l’institut Fourier

Let X be a Banach space with a countable unconditional basis (e.g., X = ℓ 2 ), Ω ⊂ X an open set and f 1 , ... , f k complex-valued holomorphic functions on Ω , such that the Fréchet differentials d f 1 ( x ) , ... , d f k ( x ) are linearly independant over ℂ at each x ∈ Ω . We suppose that M = { x ∈ Ω : f 1 ( x ) = ... = f k ( x ) = 0 } is a complete intersection and we consider a holomorphic Banach vector bundle E → M . If I (resp. 𝒪 E ) denote the ideal of germs of holomorphic functions on Ω that vanish on M (resp. the sheaf of germs of holomorphic sections of E ), then the sheaf cohomology groups H q ( Ω , I ) , H q ( M , 𝒪 E ) vanish...

Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains

Kazimierz Włodarczyk (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

An infinite dimensional extension of the Pick-Julia theorem is used to derive the conditions of Carathéodory type which guarantee the existence of angular limits and angular derivatives for holomorphic maps of infinite dimensional bounded symmetric homogeneous domains in J * -algebras and in complex Hilbert spaces. The case of operator-valued analytic maps is considered and examples are given.

Applications sommantes et radonifiantes

Patrice Assouad (1972)

Annales de l'institut Fourier

Soient E , F des espaces de Banach L ϕ , L ψ des espaces d’Orlicz, on définit les applications ϕ - ψ sommantes de E dans F . On montre que de telles applications sont ϕ - ψ radonifiantes de E dans σ ( F ' ' , F ' ) .On donne une factorisation caractéristique des applications ϕ - 0 sommantes.

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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