Constructing continuous functions holomorphic off a curve

Christopher J. Bishop

doi:10.1016/0022-1236(89)90094-3

Constructing continuous functions holomorphic off a curve

Christopher J. Bishop

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We give new proofs of a theorem of A. Browder and J. Wermer and a theorem of A. Davie which characterize the plane sets K for which A_K is a Dirichlet algebra. The use of functional analysis in the original proofs is replaced by a construction involving bounded solutions of the \ ̄t6 equation. In particular, this gives an explicit construction of nonconstant functions in these spaces.

Original language	English
Pages (from-to)	113-137
Number of pages	25
Journal	Journal of Functional Analysis
Volume	82
Issue number	1
DOIs	https://doi.org/10.1016/0022-1236(89)90094-3
State	Published - Jan 1989

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AB - We give new proofs of a theorem of A. Browder and J. Wermer and a theorem of A. Davie which characterize the plane sets K for which AK is a Dirichlet algebra. The use of functional analysis in the original proofs is replaced by a construction involving bounded solutions of the \ ̄t6 equation. In particular, this gives an explicit construction of nonconstant functions in these spaces.

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DO - 10.1016/0022-1236(89)90094-3

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Constructing continuous functions holomorphic off a curve

Abstract

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