Vol. 125, No. 2, 1986

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Plane curves and removable sets

Robert P. Kaufman

Vol. 125 (1986), No. 2, 409–413
Abstract

Various function spaces defined outside a curve Γ are introduced, along with their subspaces of holomorphic functions. The removability of Γ depends on the modulus of continuity; the results obtained are quite precise, as shown by examples based on careful estimation of Fourier coefficients. It is most surprising that the results are nearly the same for the holomorphic functions, and even for functions conformal off Γ.

Mathematical Subject Classification 2000
Primary: 30B40
Secondary: 26E05, 30D40
Milestones
Received: 29 June 1985
Published: 1 December 1986
Authors
Robert P. Kaufman