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Infinite dimensional holomorphy and applications
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Functional Analysis, Holomorphy and Approximation Theory
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This book presents a set of basic properties of holomorphic mappings between complex normed spaces and between complex locally convex spaces. These properties have already achieved an almost definitive form and should be known to all those interested in the study of infinite dimensional Holomorphy and its applications.The author also makes ``incursions'' into the study of the topological properties of the spaces of holomorphic mappings between spaces of infinite dimension. An attempt is then made to show some of the several topologies that can naturally be considered in these spaces.
Normed linear spaces.
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Domains of holomorphy.
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Holomorphy domains
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Analytic continuation
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Functions of several complex variables
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Linear normed spaces
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Normed vector spaces
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Banach spaces
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Functional analysis
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Vector analysis
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Problems arising from the study of holomorphic continuation and holomorphic approximation have been central in the development of complex analysis in finitely many variables, and constitute one of the most promising lines of research in infinite dimensional complex analysis. This book presents a unified view of these topics in both finite and infinite dimensions.
Banach spaces. --- Domains of holomorphy. --- Holomorphic functions. --- Functions, Holomorphic --- Functions of several complex variables --- Holomorphy domains --- Analytic continuation --- Functions of complex variables --- Generalized spaces --- Topology
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Foliacions (Matemàtica) --- Topologia diferencial --- Foliations (Mathematics) --- Domains of holomorphy. --- Algebraic topology. --- Topology --- Holomorphy domains --- Analytic continuation --- Functions of several complex variables --- Foliated structures --- Differential topology
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Symplectic geometry. --- Symplectic groups. --- Domains of holomorphy. --- Géométrie symplectique. --- Groupes symplectiques. --- Domaines d'holomorphie. --- Géométrie symplectique --- Groupes symplectiques --- Domaines d'holomorphie --- Symplectic geometry --- Symplectic groups --- Domains of holomorphy --- Holomorphy domains --- Analytic continuation --- Functions of several complex variables --- Groups, Symplectic --- Linear algebraic groups --- Geometry, Differential
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Holomorphic maps and invariant distances
Analytical spaces --- Banach spaces. --- Holomorphic mappings. --- Domains of holomorphy. --- Distance geometry. --- Abstract metrics --- Metric topology --- Metric spaces --- Topology --- Holomorphy domains --- Analytic continuation --- Functions of several complex variables --- Mappings, Holomorphic --- Mappings (Mathematics) --- Functions of complex variables --- Generalized spaces --- Banach spaces --- Distance geometry --- Domains of holomorphy --- Holomorphic mappings --- 517.55 --- 517.982 --- 517.982 Linear spaces with topology and order or other structures --- Linear spaces with topology and order or other structures --- 517.55 Functions of several complex variables. Approximation. Integral representations. Holomorphic functions. Entire functions --- Functions of several complex variables. Approximation. Integral representations. Holomorphic functions. Entire functions
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