Die Nuklearität der Ultradistributionsräume und der Satz vom Kern. I

DOI10.1007/BF01310050zbMath0373.46052OpenAlexW4236106247MaRDI QIDQ1244687

Hans-Joachim Petzsche

Publication date: 1978

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/154538

Mathematics Subject Classification ID

Sequence spaces (including Köthe sequence spaces) (46A45) General theory of locally convex spaces (46A03) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Tensor products in functional analysis (46M05)

Related Items (18)

On two classes of (F)-spaces ⋮ Negative results on the Nash-Moser theorem for Köthe sequence spaces and for spaces of ultradifferentiable functions ⋮ Continuation of functionals on ultradifferentiable function spaces ⋮ Generalized Fourier expansions for zero-solutions of surjective convolution operators on \({\mathcal D}_\{\omega\}({\mathbb{R}})'\) ⋮ Kernel theorems for Beurling-Björck type spaces ⋮ Global hypoelliptic vector fields in ultradifferentiable classes and normal forms ⋮ Holomorphic approximation of ultradifferentiable functions ⋮ Generalized Function Algebras Containing Spaces of Periodic Ultradistributions ⋮ Ein Isomorphiesatz für Potenzreihenräume ⋮ Characterization of nuclearity for Beurling–Björck spaces ⋮ The nuclearity of Gelfand-Shilov spaces and kernel theorems ⋮ Inverse closed ultradifferential subalgebras ⋮ Global regularity in ultradifferentiable classes ⋮ Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis ⋮ Moment sequences for ultradistributions ⋮ Almost analytic extension of ultradifferentiable functions and the boundary values of holomorphic functions ⋮ Quasi-analyticity for hypoelliptic operators ⋮ Discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type

Cites Work

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• Théorie des distributions à valeurs vectorielles
• On the intersection of classes of infinitely differentiable functions
• Sur la topologie des espaces de fonctions holomorphes
• Einführung in die Theorie der lokalkonvexen Räume
• Linear partial differential operators and generalized distributions
• Ultra-distributions definies sur \(R^ n\) et sur certaines classes de variétés différentiables
• Analytic Extensions of Differentiable Functions Defined in Closed Sets
• On 𝜆-nuclearity
• Folgenretraktive Sequenzen lokalkonvexer Räume.

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