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    Boundary Smoothness of Analytic Functions


    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: 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:

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