000 03218nam a22005415i 4500
001 978-3-540-46396-2
003 DE-He213
005 20190213151548.0
007 cr nn 008mamaa
008 121227s1991 gw | s |||| 0|eng d
020 _a9783540463962
_9978-3-540-46396-2
024 7 _a10.1007/BFb0089147
_2doi
050 4 _aQA612-612.8
072 7 _aPBPD
_2bicssc
072 7 _aMAT038000
_2bisacsh
072 7 _aPBPD
_2thema
082 0 4 _a514.2
_223
100 1 _aBanaszczyk, Wojciech.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aAdditive Subgroups of Topological Vector Spaces
_h[electronic resource] /
_cby Wojciech Banaszczyk.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1991.
300 _aVII, 182 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1466
505 0 _aPreliminaries -- Exotic groups -- Nuclear groups -- The bochner theorem -- Pontryagin duality.
520 _aThe 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.
650 0 _aAlgebraic topology.
650 0 _aFunctional analysis.
650 0 _aTopological Groups.
650 0 _aGlobal analysis (Mathematics).
650 1 4 _aAlgebraic Topology.
_0http://scigraph.springernature.com/things/product-market-codes/M28019
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aDiscrete Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/M29000
650 2 4 _aTopological Groups, Lie Groups.
_0http://scigraph.springernature.com/things/product-market-codes/M11132
650 2 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662215265
776 0 8 _iPrinted edition:
_z9783540539179
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1466
856 4 0 _uhttps://doi.org/10.1007/BFb0089147
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11108
_d11108