Real analytic curves in Fréchet spaces and their duals

DOI10.1007/BF01312453zbMath0918.46034OpenAlexW2324523844MaRDI QIDQ1264302

José Bonet, Paweł Domański

Publication date: 4 August 1999

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178822

zbMATH Keywords

Fréchet spacesStein manifoldsLiouville propertytensor product representationfirst derived functor of the functor of projective limitgerm of holomorphic functionsLB-spacesparameter dependence of solutionssurjective convolution operatorvector-valued real analytic mapsvector-valued Taylor series

Mathematics Subject Classification ID

Spaces of vector- and operator-valued functions (46E40) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Locally convex Fréchet spaces and (DF)-spaces (46A04) Spaces of linear operators; topological tensor products; approximation properties (46A32) Categories, functors in functional analysis (46M15) Power series, series of functions of several complex variables (32A05) Holomorphic functions of several complex variables (32A10) Applications of functional analysis to differential and integral equations (46N20) Tensor products in functional analysis (46M05) PDEs of infinite order (35R50)

Related Items (16)

Bounded tightness for locally convex spaces and spaces \(C(X)\) ⋮ Strong duals of projective limits of (LB)-spaces ⋮ Tightness and distinguished Fréchet spaces ⋮ Solution to the first Cousin problem for vector-valued quasianalytic functions ⋮ Real analytic parameter dependence of solutions of differential equations over Roumieu classes ⋮ Power bounded composition operators on spaces of analytic functions ⋮ Factorization in Denjoy-Carleman classes associated to representations of \((\mathbb{R}^d, +)\) ⋮ Non-quasianalytic curves in Fréchet spaces ⋮ Splitting and parameter dependence in the category of \(\mathrm{PLH}\) spaces ⋮ The splitting of exact sequences of PLS-spaces and smooth dependence of solutions of linear partial differential equations ⋮ Superposition in classes of ultradifferentiable functions ⋮ Real analytic parameter dependence of solutions of differential equations ⋮ Vector valued hyperfunctions and boundary values of vector valued harmonic and holomorphic functions ⋮ The Levy-Steinitz rearrangement theorem for duals of metrizable spaces ⋮ Parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences ⋮ Parameter dependence of solutions of partial differential equations in spaces of real analytic functions

Cites Work

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• Partial differential operators depending analytically on a parameter
• Operators with closed ranges in spaces of analytic vector-valued functions
• On two classes of (F)-spaces
• Inversion von Fredholmfunktionen bei stetiger und holomorpher Abhängigkeit von Parametern
• Vektorwertige Distributionen als Randverteilungen holomorpher Funktionen
• On the convenient setting for real analytic mappings
• Complete projective tensor product of (LB)-spaces
• A sufficient condition for \(\text{Proj}^1\chi=0\)
• The convenient setting for real analytic mappings
• On the existence of real analytic solutions of partial differential equations with constant coefficients
• Hyperfunction fundamental solutions of surjective convolution operators on real analytic functions
• A sufficient condition for vanishing of the derived projective limit functor
• Sur les fonctionnelles analytiques et la transformation de Fourier-Borel
• Sur la topologie des espaces de fonctions holomorphes
• Randverteilungen analytischer Funktionen und Distributionen
• Frécheträume, zwischen denen jede stetige lineare Abbildung beschränkt ist.
• Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals.
• A Projective Description of Weighted Inductive Limits
• Fundamental Solutions for Hypoelliptic Differential Operators Depending Analytically on a Parameter
• BANACH Coherent Analytic FRÉCHET Sheaves
• Continuous linear right inverses for convolution operators in spaces of real analytic functions
• Characterization of the Linear Partial Differential Operators with Constant Coefficients Which are Surjective on Non‐quasianalytic Classes of Roumieu Type on ℝ^N
• Analytic functions in topological vector-spaces
• Acyclic inductive spectra of Fréchet spaces
• Produits tensoriels topologiques et espaces nucléaires
• On analytic vector-valued functions of a real variable

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