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

 

Some characterizations of $C(\mathcal M)$


Author: Christopher J. Bishop
Journal: Proc. Amer. Math. Soc. 124 (1996), 2695-2701
MSC (1991): Primary 46J10
MathSciNet review: 1326997
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Abstract: We show that a function $f$ on the unit disk extends continuously to $\mathcal M$, the maximal ideal space of $H^\infty (\mathbb D)$ iff it is uniformly continuous (in the hyperbolic metric) and close to constant on the complementary components of some Carleson contour.


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Additional Information

Christopher J. Bishop
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651
Email: bishop@math.sunysb.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03328-X
PII: S 0002-9939(96)03328-X
Keywords: Harmonic functions, holomorphic functions, function algebras, maximal ideal space, Carleson measures, uniform approximation
Received by editor(s): November 23, 1994
Received by editor(s) in revised form: February 24, 1995
Additional Notes: The author is partially supported by NSF Grant DMS 92-04092 and an Alfred P. Sloan research fellowship.
Communicated by: T. W. Gamelin
Article copyright: © Copyright 1996 American Mathematical Society