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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

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