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Nuclear space

In mathematics, nuclear spaces are topological vector spaces that can be viewed as a generalization of finite-dimensional Euclidean spaces and share many of their desirable properties. Nuclear spaces are however quite different from Hilbert spaces, another generalization of finite-dimensional Euclidean spaces. They were introduced by Alexander Grothendieck.

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Overview

Original motivation: The Schwartz kernel theorem

Definition

Characterizations

Sufficient conditions

Properties

Bochner–Minlos theorem

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Map overview Semantic statistics

Nuclear space

Nodes60
Edges59
Triples74
Avg. degree1.97
Density0.033333
Components1

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Nuclear space

Top relations

related to Properties · 14
Nuclear space → Any, Every, Fréchet, Hausdorff, Heine-Borel, Hilbert, If, In, Montel, Nuclear, Radon, Roughly, Schwartz, This
related to Original motivation: The Schwartz kernel theorem · 11
Nuclear space → Alexander Grothendieck, For, Grothendieck, In, Much, Omega, Schwartz, TVS-isomorphic, TVS-isomorphisms, TVSs, We
related to The kernel theorem · 9
Nuclear space → Alexander Grothendieck, Equivalently, Furthermore, Grothendieck, Much, Schwartz, Suppose, Then, We
related to Characterizations · 8
Nuclear space → Banach, Hausdorff, Hilbert, Let, Schmidt, Then, TVS-isomorphism, TVSs
related to Sufficient conditions · 7
Nuclear space → Every, Every Hausdorff, Fréchet, Hausdorff, In, Suppose, The
is a · 6
Nuclear space → compact metrizable set, locally convex topological vector space such that for any seminorm p, locally convex topological vector space such that for every seminorm p, set of smooth functions on a compact manifold, space of all rapidly decreasing sequences c, topological vector space with a topology defined by a family of Hilbert seminorms
related to Bochner–Minlos theorem · 6
Nuclear space → Any, Bochner, Given, Minlos, Robert Adol'fovich Minlos, Salomon Bochner
related to Definition · 5
Nuclear space → Fréchet, Grothendieck, Note, The, This
related to Examples · 5
Nuclear space → For, If, In, Rapidly, So
related to Motivations from geometry · 3
Nuclear space → Another, Given, Hausdorff

Important terminology Word statistics

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Important terminology

nuclear space displaystyle spaces vector every convex topological locally map topology hilbert product dual prime seminorm banach definition seminorms natural

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Nuclear spaceis aset of smooth functions on a compact manifold0.90text
Nuclear spaceis alocally convex topological vector space such that for every seminorm p0.90text
Nuclear spaceis atopological vector space with a topology defined by a family of Hilbert seminorms0.90text
Nuclear spaceis aspace of all rapidly decreasing sequences c0.90text
Nuclear spaceis acompact metrizable set0.90text
Nuclear spaceis alocally convex topological vector space such that for any seminorm p0.90text
Nuclear spacerelated to Bochner–Minlos theoremAny0.60section
Nuclear spacerelated to Bochner–Minlos theoremGiven0.60section
Nuclear spacerelated to Bochner–Minlos theoremBochner0.60section
Nuclear spacerelated to Bochner–Minlos theoremMinlos0.60section
Nuclear spacerelated to Bochner–Minlos theoremSalomon Bochner0.60section
Nuclear spacerelated to Bochner–Minlos theoremRobert Adol'fovich Minlos0.60section

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    Min side: 3
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