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Schwartz kernel theorem

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 D {\displaystyle…

Art, Integral kernels & Statement of the theorem

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Integral kernels

Kernel functionsIntegral operatorsDual spaceDirac delta functionCompact operators
12 related topics

Statement of the theorem

DistributionContinuous linear mapIntegral transform
3 related topics

Generalization to nuclear spaces

NuclearAlexander GrothendieckGrothendieck 1955
3 related topics

Smooth manifolds

Smooth manifolds
1 related topics

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Statement of the theorem

Integral kernels

Smooth manifolds

Generalization to nuclear spaces

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Schwartz kernel theorem

Nodes42
Edges41
Triples10
Avg. degree1.95
Density0.047619
Components1

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Schwartz kernel theorem

Top relations

related to Generalization to nuclear spaces · 8
Schwartz kernel theorem → Alexander Grothendieck, Equivalently, Grothendieck, Much, Schwartz, Suppose, Then, We
is a · 1
Schwartz kernel theorem → foundational result in the theory of generalized functions

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Important terminology

displaystyle nuclear kernel schwartz theory space mathcal functions theorem distribution spaces operators distributions integral oclc isbn linear form result bilinear

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Schwartz kernel theoremis afoundational result in the theory of generalized functions0.90text
the continuous functions oninstance ofonly compact operators are created on a space0.80text
Schwartz kernel theoremrelated to Generalization to nuclear spacesMuch0.60section
Schwartz kernel theoremrelated to Generalization to nuclear spacesAlexander Grothendieck0.60section
Schwartz kernel theoremrelated to Generalization to nuclear spacesSchwartz0.60section
Schwartz kernel theoremrelated to Generalization to nuclear spacesGrothendieck0.60section
Schwartz kernel theoremrelated to Generalization to nuclear spacesWe0.60section
Schwartz kernel theoremrelated to Generalization to nuclear spacesSuppose0.60section
Schwartz kernel theoremrelated to Generalization to nuclear spacesThen0.60section
Schwartz kernel theoremrelated to Generalization to nuclear spacesEquivalently0.60section

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