Displaying similar documents to “Hypersurfaces of inifnite dimensional Banach spaces, Bertini theorems and embeddings of projective spaces.”

Infinite-dimensional complex projective spaces and complete intersections

Edoardo Ballico (2006)

Mathematica Bohemica

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Let V be an infinite-dimensional complex Banach space and X ⊂ 𝐏 ( V ) a closed analytic subset with finite codimension. We give a condition on X which implies that X is a complete intersection. We conjecture that the result should be true for more general topological vector 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 .

Characterization of surjective partial differential operators on spaces of real analytic functions

Michael Langenbruch (2004)

Studia Mathematica

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Let A(Ω) denote the real analytic functions defined on an open set Ω ⊂ ℝⁿ. We show that a partial differential operator P(D) with constant coefficients is surjective on A(Ω) if and only if for any relatively compact open ω ⊂ Ω, P(D) admits (shifted) hyperfunction elementary solutions on Ω which are real analytic on ω (and if the equation P(D)f = g, g ∈ A(Ω), may be solved on ω). The latter condition is redundant if the elementary solutions are defined on conv(Ω). This extends and improves...