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Locally Convex Structure of Some Algebras of Holomorphic Functions of Several Variables
Author(s) -
Nawrocki Marek
Publication year - 2002
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 - 10.1002/1522-2616(200212)246:1<170::aid-mana170>3.0.co;2-0
Subject(s) - polydisc , mathematics , hardy space , unit sphere , pure mathematics , sequence (biology) , bergman space , unit (ring theory) , combinatorics , space (punctuation) , convex domain , envelope (radar) , regular polygon , mathematical analysis , geometry , bounded function , holomorphic function , linguistics , genetics , mathematics education , philosophy , biology , telecommunications , radar , computer science
In the paper a general method is developed which allows to show that a nuclear Köthe space is a Fréchet envelope of another “sequence space”. Applying this method we describe the locally convex structure of Hardy N p * ( D ), maximal Hardy MN p * ( D ), Bergman p ( D ), and Lumer's Hardy LN p * ( D ) algebras of any domain D being a product of balls in ℂ n i(in particular for the unit ball and the unit polydisc in ℂ n ).