About: Schwartz kernel theorem

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In mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952. It states, in broad terms, that the generalized functions introduced by Schwartz (Schwartz distributions) have a two-variable theory that includes all reasonable bilinear forms on the space of test functions. The space itself consists of smooth functions of compact support.

Attributes	Values
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rdfs:label	Kernsatz von Schwartz (de) Schwartz kernel theorem (en)
rdfs:comment	Der Kernsatz von Schwartz (oder Satz vom Kern) ist eine wichtige mathematische Aussage im Bereich der Distributionentheorie, welche ein Teilgebiet der Funktionalanalysis ist. Sie wurde von dem Mathematiker Laurent Schwartz im Jahr 1952 bewiesen. Diese Aussage wird jedoch nicht auf Grund ihrer Wichtigkeit Kernsatz genannt, sondern weil es sich um eine Aussage über Integralkerne handelt. Diese hier behandelten Integralkerne werden Schwartz-Kerne genannt. (de) In mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952. It states, in broad terms, that the generalized functions introduced by Schwartz (Schwartz distributions) have a two-variable theory that includes all reasonable bilinear forms on the space of test functions. The space itself consists of smooth functions of compact support. (en)
dcterms:subject	Generalized functions Theorems in functional analysis Transforms
Wikipage page ID	7646018 (xsd:integer)
Wikipage revision ID	1055904643 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective tensor product Pseudo-differential operator Rigged Hilbert space Bilinear form Generalized functions Integral operator Compact support Theorems in functional analysis Mathematics Nuclear operator Nuclear space Generalized function Singular support Smooth function Compact operator Functional analysis Alexander Grothendieck Dual space Differential operator Jean Dieudonné Transforms Laurent Schwartz Trace class Dirac delta function Fredholm kernel Schwartz distribution Injective tensor product Smooth manifold Test functions Kernel function Support of a function
sameAs	Schwartz kernel theorem Schwartz kernel theorem Schwartz kernel theorem Schwartz kernel theorem Schwartz kernel theorem
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Grothendieck_Produits_Tensoriels_Topologiques_et_Espaces_Nucléaires dbt:Cite_book dbt:NumBlk dbt:Reflist dbt:Sfn dbt:EquationRef dbt:Harvnb dbt:EquationNote dbt:Functional_analysis dbt:Schaefer_Wolff_Topological_Vector_Spaces dbt:Trèves_François_Topological_vector_spaces,_distributions_and_kernels
author	G. L. Litvinov (en)
id	N/n067820 (en)
title	Nuclear bilinear form (en)
has abstract	Der Kernsatz von Schwartz (oder Satz vom Kern) ist eine wichtige mathematische Aussage im Bereich der Distributionentheorie, welche ein Teilgebiet der Funktionalanalysis ist. Sie wurde von dem Mathematiker Laurent Schwartz im Jahr 1952 bewiesen. Diese Aussage wird jedoch nicht auf Grund ihrer Wichtigkeit Kernsatz genannt, sondern weil es sich um eine Aussage über Integralkerne handelt. Diese hier behandelten Integralkerne werden Schwartz-Kerne genannt. (de) In mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952. It states, in broad terms, that the generalized functions introduced by Schwartz (Schwartz distributions) have a two-variable theory that includes all reasonable bilinear forms on the space of test functions. The space itself consists of smooth functions of compact support. (en)
gold:hypernym	Result
prov:wasDerivedFrom	wikipedia-en:Schwartz_kernel_theorem?oldid=1055904643&ns=0
page length (characters) of wiki page	7027 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Schwartz_kernel_theorem
is Link from a Wikipage to another Wikipage of	Valuation (geometry) Integral transform Nuclear space Laurent Schwartz Spaces of test functions and distributions Schwartz's kernel theorem List of theorems Oscillatory integral Schur test
is Wikipage redirect of	Schwartz's kernel theorem
is known for of	Laurent Schwartz
is known for of	Laurent Schwartz
is foaf:primaryTopic of	wikipedia-en:Schwartz_kernel_theorem

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