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On a Bornological Structure in Infinite‐Dimensional Holomorphy
Author(s) -
Bjon S.,
Lindström M.
Publication year - 1988
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19881390108
Subject(s) - holomorphic function , mathematics , bounded function , connection (principal bundle) , pure mathematics , infinite dimensional holomorphy , locally convex topological vector space , regular polygon , convergence (economics) , space (punctuation) , mathematical analysis , banach space , geometry , topological space , lp space , banach manifold , linguistics , philosophy , economics , economic growth
The bornology ( b ) of bounded subsets with respect to continuous convergence is used on spaces of holomorphic functions. It is shown that Hom co H b ( U ) ≅ U for a circled convex open subset U of a complete nuclear space. Exponential laws for spaces of holomorphic functions with bornological structures are proved and the connection with Colombeau's Silva holomorphic functions is established.