Generalized function algebras as sequence space algebras

DOI10.1090/S0002-9939-04-07306-XzbMath1052.46002arXivmath/0206039OpenAlexW2993937457MaRDI QIDQ4461120

Stevan Pilipović, Antoine Delcroix, Maximilian F. Hasler, Vincent S. Valmorin

Publication date: 29 March 2004

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0206039

zbMATH Keywords

ultrametricsdiscrete topologyembedded Dirac delta distributionsequences of exponential weights

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Sequence spaces (including Köthe sequence spaces) (46A45) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Compactness in topological linear spaces; angelic spaces, etc. (46A50)

Related Items (14)

Generalized functions as sequence spaces with ultranorms ⋮ Sheaves of nonlinear generalized functions and manifold-valued distributions ⋮ New topologies on Colombeau generalized numbers and the Fermat-Reyes theorem ⋮ The functional analytic foundation of Colombeau algebras ⋮ Isomorphisms of algebras of generalized functions ⋮ Compatibility conditions and the convolution of functions and generalized functions ⋮ New sequence spaces and function spaces on interval \([0, 1\)] ⋮ Hilbert $\widetilde{\mathbb{C}}$-modules: Structural properties and applications to variational problems ⋮ Homogeneity in generalized function algebras ⋮ Harmonic generalized functions in generalized function algebras ⋮ Generalized integral operators and Schwartz kernel type theorems ⋮ Weak homogeneity in generalized function algebras ⋮ Pointwise characterizations in generalized function algebras ⋮ Asymptotic extension of topological modules and algebras

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