Displaying similar documents to “On the ∂ ¯ -equation in a Banach space”

Approximation of holomorphic functions of infinitely many variables II

László Lempert (2000)

Annales de l'institut Fourier

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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.

Bounded analytic sets in Banach spaces

Volker Aurich (1986)

Annales de l'institut Fourier

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Conditions are given which enable or disable a complex space X to be mapped biholomorphically onto a bounded closed analytic subset of a Banach space. They involve on the one hand the Radon-Nikodym property and on the other hand the completeness of the Caratheodory metric of X .

Schwarz-type lemmas for solutions of ∂ ¯ -inequalities and complete hyperbolicity of almost complex manifolds

Sergey Ivashkovich, Jean-Pierre Rosay (2004)

Annales de l'Institut Fourier

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The definition of the Kobayashi-Royden pseudo-metric for almost complex manifolds is similar to its definition for complex manifolds. We study the question of completeness of some domains for this metric. In particular, we study the completeness of the complement of submanifolds of co-dimension 1 or 2. The paper includes a discussion, with proofs, of basic facts in the theory of pseudo-holomorphic discs.

Analytic cohomology of complete intersections in a Banach space

Imre Patyi (2004)

Annales de l’institut Fourier

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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...