Additive Subgroups of Topological Vector Spaces: 1466 (Lecture Notes in Mathematics, 1466) - Softcover

Banaszczyk, Wojciech

 
9783540539179: Additive Subgroups of Topological Vector Spaces: 1466 (Lecture Notes in Mathematics, 1466)
Softcover
ISBN 10: 3540539174 ISBN 13: 9783540539179
Publisher: Springer, 1991

Synopsis

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.

"synopsis" may belong to another edition of this title.

Synopsis

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. The text 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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
1991
Language
English
ISBN 10 
3540539174
ISBN 13 
9783540539179
Binding
Paperback
Number of pages
189