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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
DOI: https://doi.org/10.1090/S0002-9939-1972-0290115-6
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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Keywords: Bounded holomorphic functions, polydisc, closed boundary, Shilov boundary
Article copyright: © Copyright 1972 American Mathematical Society