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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A small boundary for $ H^{\infty }$ on the polydisc

Author: R. Michael Range
Journal: Proc. Amer. Math. Soc. 32 (1972), 253-255
MSC: Primary 46.55; Secondary 32.00
MathSciNet review: 0290115
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Abstract: Let $ {\Delta ^n}$ be the unit polydisc in $ {C^n}$ and let $ {T^n}$ be its distinguished boundary. It is shown that for $ n \geqq 2$ there is a nowhere dense subset of the maximal ideal space of $ {L^\infty }({T^n})$ which defines a closed boundary for $ {H^\infty }({\Delta ^n})$.

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PII: S 0002-9939(1972)0290115-6
Keywords: Bounded holomorphic functions, polydisc, closed boundary, Shilov boundary
Article copyright: © Copyright 1972 American Mathematical Society