ENGLISH

Additive Subgroups of Topological Vector Spaces

By Wojciech Banaszczyk (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1991
ISBN
9780387539171, 0-387-53917-4, 3540539174
DOI
10.1007/BFb0089147
LCC
QA3 .L28 no. 1466,QA322 .L28 no. 1466
Open Library ID
OL1535263M
Language
english
Format
PDF
Filesize
5 MB (5724905 bytes)
Series
Lecture Notes in Mathematics 1466
Edition
1
Pages
182\186
Library
mexmat
Time added
2009-07-20 03:45:11
Lie Groups; AnalysisTopological Groups

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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