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Constructing continuous functions holomorphic off a curve

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
82
Issue
1
Identifiers
DOI: 10.1016/0022-1236(89)90094-3
Disciplines
  • Mathematics

Abstract

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.

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