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On Sparse Sets with the Green Function of the Highest Smoothness

On Sparse Sets with the Green Function of the Highest Smoothness Let E be a regular compact subset of the real line, let [InlineMediaObject not available: see fulltext.] be the Green function of the complement of E with respect to the extended complex plane ${\overline {\rm C}}$ with pole at ∞. We construct two examples of sets E of the minimum Hausdorff dimension with [InlineMediaObject not available: see fulltext.] satisfying the Hölder condition with p = 1/2 either uniformly or locally. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

On Sparse Sets with the Green Function of the Highest Smoothness

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Publisher
Springer Journals
Copyright
Copyright © 2005 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321100
Publisher site
See Article on Publisher Site

Abstract

Let E be a regular compact subset of the real line, let [InlineMediaObject not available: see fulltext.] be the Green function of the complement of E with respect to the extended complex plane ${\overline {\rm C}}$ with pole at ∞. We construct two examples of sets E of the minimum Hausdorff dimension with [InlineMediaObject not available: see fulltext.] satisfying the Hölder condition with p = 1/2 either uniformly or locally.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

References