Holomorphic functions on fully nuclear spaces

DOI10.24033/bsmf.1875zbMath0402.46017OpenAlexW2585949680MaRDI QIDQ4186840

Seán Dineen, Philip J. Boland

Publication date: 1978

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_1978__106__311_0

zbMATH Keywords

Topological DualHolomorphic GermsCompact Ported TopologyEquicontinuous BasisFully Nuclear SpaceHolomorphic Functions on Nuclear SpacesInductive Limit Of Banach SpacesUniform Convergence on Compact Subsets

Mathematics Subject Classification ID

Infinite-dimensional holomorphy (46G20) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Inductive and projective limits in functional analysis (46M40)

Related Items

Algebras of holomorphic functions, Weakly and separately holomorphic functions on compact determining polydiscs in (DFN)-spaces, Characterization of nuclear Fréchet spaces in which every bounded set is polar, On the convergence of Gromov-Witten potentials and Givental's formula, Convolution operators on spaces of entire functions, Michael problem and algebras of holomorphic functions, Holomorphic functions on strict inductive limits, On bounded approximation properties of spaces of holomorphic functions on certain open subsets of strong duals of nuclear Frechet spaces, On unconditional bases in spaces of holomorphic functions in infinite dimensions, Reinhardt domains of holomorphy in Banach spaces, Counterexamples in holomorphic functions on nuclear Fréchet spaces, A Banach-Dieudonné theorem for germs of holomorphic functions, On the holomorphic extension of vector valued functions

Cites Work

• An example of a nuclear space in infinite dimensional holomorphy
• Holomorphic functions on locally convex topological vector spaces. I: Locally convex topologies on \({\mathcal H}(U)\)
• Holomorphic Functions on Nuclear Spaces
• Surjective limits of locally convex spaces and their application to infinite dimensional holomorphy
• Produits tensoriels topologiques et espaces nucléaires
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