02631nam 2200553 450 99646658640331620220909114401.03-540-46396-810.1007/BFb0089147(CKB)1000000000437067(DE-He213)978-3-540-46396-2(MiAaPQ)EBC5595633(Au-PeEL)EBL5595633(OCoLC)1076251900(MiAaPQ)EBC6842426(Au-PeEL)EBL6842426(OCoLC)1159606124(PPN)155191233(EXLCZ)99100000000043706720220909d1991 uy 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierAdditive subgroups of topological vector spaces /Wojciech Banaszczyk1st ed. 1991.Berlin, Germany :Springer,[1991]©19911 online resource (VII, 182 p.)Lecture Notes in Mathematics,0075-8434 ;14660-387-53917-4 3-540-53917-4 Preliminaries -- Exotic groups -- Nuclear groups -- The bochner theorem -- Pontryagin duality.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.Lecture Notes in Mathematics,0075-8434 ;1466Locally compact groupsLocally compact groups.514.243A80msc22A10mscBanaszczyk Wojciech1954-59914MiAaPQMiAaPQMiAaPQBOOK996466586403316Additive subgroups of topological vector spaces78676UNISA