Le problème du $\overline\partial$ sur un espace de Hilbert

DOI10.24033/bsmf.1893zbMath0414.46030OpenAlexW2584853654MaRDI QIDQ3049354

P.Raboin

Publication date: 1979

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=BSMF_1979__107__225_0

zbMATH Keywords

compact operatorCousin's first problemdelta-equation on a Hilbert spaceDfn spacespseudoconvexe open set

Mathematics Subject Classification ID

Infinite-dimensional holomorphy (46G20) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Pseudoconvex domains (32T99) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items

Evolution of smooth shapes and integrable systems, \(L^2\) estimates and existence theorems for the \(\overline{\partial}\) operators in infinite dimensions. I, Local factorization of differential forms on Fréchet-Schwartz spaces, The (partial d) equation in DFN spaces, Michael problem and algebras of holomorphic functions, The \(\bar\partial\)-problem for a (0,2)-form in a D.F.N. space, The Dolbeault complex in infinite dimensions I, Counterexamples in holomorphic functions on nuclear Fréchet spaces, L'équation $\bar\partial$ dans les ouverts pseudo-convexes des espaces DFN, The Dolbeault complex in infinite dimensions II

Cites Work

• The Levi problem in certain infinite dimensional vector spaces
• Potential theory on Hilbert space
• Prolongement analytique en dimension infinie. (Analytic extension in infinite dimension)
• The \(\bar \partial\) equation with polynomial growth on a Hilbert space
• The theory of differentiation in linear topological spaces
• Holomorphic Functions on Nuclear Spaces
• A Divergence Theorem for Hilbert Space
• Smooth Partitions of Unity on Manifolds
• The First Variation of an Indefinite Wiener Integral
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