O'Farrell, Anthony G.
(2014)
Boundary Smoothness of Analytic Functions.
Analysis and Mathematical Physics, 4 (1-2).
pp. 131-144.
ISSN 1664-2368
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: |
https://doi.org/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 |
| URI: |
|
| 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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