LEADER 02631nam 2200553 450 001 996466586403316 005 20220909114401.0 010 $a3-540-46396-8 024 7 $a10.1007/BFb0089147 035 $a(CKB)1000000000437067 035 $a(DE-He213)978-3-540-46396-2 035 $a(MiAaPQ)EBC5595633 035 $a(Au-PeEL)EBL5595633 035 $a(OCoLC)1076251900 035 $a(MiAaPQ)EBC6842426 035 $a(Au-PeEL)EBL6842426 035 $a(OCoLC)1159606124 035 $a(PPN)155191233 035 $a(EXLCZ)991000000000437067 100 $a20220909d1991 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAdditive subgroups of topological vector spaces /$fWojciech Banaszczyk 205 $a1st ed. 1991. 210 1$aBerlin, Germany :$cSpringer,$d[1991] 210 4$d©1991 215 $a1 online resource (VII, 182 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1466 311 $a0-387-53917-4 311 $a3-540-53917-4 327 $aPreliminaries -- Exotic groups -- Nuclear groups -- The bochner theorem -- Pontryagin duality. 330 $aThe Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a nuclear group, which includes LCA groups and nuclear locally convex spaces together with their additive subgroups, quotient groups and products. For (metrizable, complete) nuclear groups one obtains analogues of the Pontryagin duality theorem, of the Bochner theorem and of the Lévy-Steinitz theorem on rearrangement of series (an answer to an old question of S. Ulam). The book is written in the language of functional analysis. The methods used are taken mainly from geometry of numbers, geometry of Banach spaces and topological algebra. The reader is expected only to know the basics of functional analysis and abstract harmonic analysis. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1466 606 $aLocally compact groups 615 0$aLocally compact groups. 676 $a514.2 686 $a43A80$2msc 686 $a22A10$2msc 700 $aBanaszczyk$b Wojciech$f1954-$059914 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466586403316 996 $aAdditive subgroups of topological vector spaces$978676 997 $aUNISA