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Smoothness of analytic
functions at boundary points
Mikihiro Hayashi |
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Vol. 67 (1976), No. 1, 171–202
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Abstract |
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Let U be a bounded open set in the plane. We study the smoothness at boundary points of the continuous functions on U which are analytic in U. A main result is the characterization of sequences xn ∈U, xn → x, with the property that the functions are of class Ck along xn at x. As an application of this characterization, we can find an open set U for any twice continuously differentiable arc J such that U contains J in its boundary and the functions are of class C∞ on J. |
Mathematical Subject Classification 2000
Primary: 30A72, 30A72
Secondary: 46J15, 30A98
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Milestones
Received: 15 September 1975
Revised: 6 July 1976
Published: 1 November 1976
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Authors |
| Mikihiro Hayashi | |
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