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O'Farrell, Anthony G. (2014) Boundary Smoothness of Analytic Functions. Analysis and Mathematical Physics, 4 (1-2). pp. 131-144. ISSN 1664-2368
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Abstract
We consider the behaviour of holomorphic functions
on a bounded open subset of the plane, satisfying a Lipschitz con-
dition with exponent α, with 0 < α < 1, in the vicinity of an
exceptional boundary point where all such functions exhibit some
kind of smoothness. Specifically, we consider the relation between
the abstract idea of a bounded point derivation on the algebra of
such functions and the classical complex derivative evaluated as a
limit of difference quotients. We obtain a result which applies, for
example, when the open set admits an interior cone at the special
boundary point.
| Item Type: | Article |
|---|---|
| Additional Information: | This is the preprint version of the published article, which is available at DOI: 10.1007/s13324-014-0074-0 . Dedicated to Lawrence Zalcman on the occasion of his 70th birthday |
| Keywords: | Analytic function; Boundary; Lipschitz condition; Point derivation; 30E25; 30H99; 46J10; |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 6270 |
| Identification Number: | 10.1007/s13324-014-0074-0 |
| Depositing User: | Prof. Anthony O'Farrell |
| Date Deposited: | 17 Jul 2015 14:50 |
| Journal or Publication Title: | Analysis and Mathematical Physics |
| Publisher: | Springer |
| Refereed: | Yes |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/6270 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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