About: Spaces of test functions and distributions

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In mathematical analysis, the spaces of test functions and distributions are topological vector spaces (TVSs) that are used in the definition and application of distributions. Test functions are usually infinitely differentiable complex-valued (or sometimes real-valued) functions on a non-empty open subset that have compact support. The space of all test functions, denoted by is endowed with a certain topology, called the canonical LF-topology, that makes into a complete Hausdorff locally convex TVS. The strong dual space of is called the space of distributions on and is denoted by where the "" subscript indicates that the continuous dual space of denoted by is endowed with the strong dual topology.

Attributes	Values
rdf:type	Thing
rdfs:label	Spaces of test functions and distributions (en)
rdfs:comment	In mathematical analysis, the spaces of test functions and distributions are topological vector spaces (TVSs) that are used in the definition and application of distributions. Test functions are usually infinitely differentiable complex-valued (or sometimes real-valued) functions on a non-empty open subset that have compact support. The space of all test functions, denoted by is endowed with a certain topology, called the canonical LF-topology, that makes into a complete Hausdorff locally convex TVS. The strong dual space of is called the space of distributions on and is denoted by where the "" subscript indicates that the continuous dual space of denoted by is endowed with the strong dual topology. (en)
rdfs:seeAlso	Continuous linear functional LF-space Strong dual space
name	Theorem (en) Theorem. (en) Fubini's theorem for distributions (en) Schwartz kernel theorem (en)
foaf:depiction
dcterms:subject	Generalized functions Topological vector spaces Generalizations of the derivative Functional analysis Smooth functions
Wikipage page ID	67789038 (xsd:integer)
Wikipage revision ID	1108009033 (xsd:integer)
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