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Additive subgroups of topological vector spaces

The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a n...

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Autor principal: Banaszczyk, Wojciech
Lenguaje:eng
Publicado: Springer 1991
Materias:
Acceso en línea:https://dx.doi.org/10.1007/BFb0089147
http://cds.cern.ch/record/1691460
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author Banaszczyk, Wojciech
author_facet Banaszczyk, Wojciech
author_sort Banaszczyk, Wojciech
collection CERN
description The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a nuclear group, which includes LCA groups and nuclear locally convex spaces together with their additive subgroups, quotient groups and products. For (metrizable, complete) nuclear groups one obtains analogues of the Pontryagin duality theorem, of the Bochner theorem and of the Lévy-Steinitz theorem on rearrangement of series (an answer to an old question of S. Ulam). The book is written in the language of functional analysis. The methods used are taken mainly from geometry of numbers, geometry of Banach spaces and topological algebra. The reader is expected only to know the basics of functional analysis and abstract harmonic analysis.
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spelling cern-16914602021-04-21T21:09:46Zdoi:10.1007/BFb0089147http://cds.cern.ch/record/1691460engBanaszczyk, WojciechAdditive subgroups of topological vector spacesMathematical Physics and MathematicsThe Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a nuclear group, which includes LCA groups and nuclear locally convex spaces together with their additive subgroups, quotient groups and products. For (metrizable, complete) nuclear groups one obtains analogues of the Pontryagin duality theorem, of the Bochner theorem and of the Lévy-Steinitz theorem on rearrangement of series (an answer to an old question of S. Ulam). The book is written in the language of functional analysis. The methods used are taken mainly from geometry of numbers, geometry of Banach spaces and topological algebra. The reader is expected only to know the basics of functional analysis and abstract harmonic analysis.Springeroai:cds.cern.ch:16914601991
spellingShingle Mathematical Physics and Mathematics
Banaszczyk, Wojciech
Additive subgroups of topological vector spaces
title Additive subgroups of topological vector spaces
title_full Additive subgroups of topological vector spaces
title_fullStr Additive subgroups of topological vector spaces
title_full_unstemmed Additive subgroups of topological vector spaces
title_short Additive subgroups of topological vector spaces
title_sort additive subgroups of topological vector spaces
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/BFb0089147
http://cds.cern.ch/record/1691460
work_keys_str_mv AT banaszczykwojciech additivesubgroupsoftopologicalvectorspaces