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Completeness of Spaces of Harmonic Functions under Restricted Supremum Norms

Completeness of Spaces of Harmonic Functions under Restricted Supremum Norms Let E be a subset of a domain Ω in Euclidean space. This note verifies a conjecture of Arcozzi and Björn concerning the completeness of the space of harmonic functions u on Ω that are bounded on E, where the supremum norm is taken with respect to the restriction of u to E. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Completeness of Spaces of Harmonic Functions under Restricted Supremum Norms

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Publisher
Springer Journals
Copyright
Copyright © 2004 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/BF03321054
Publisher site
See Article on Publisher Site

Abstract

Let E be a subset of a domain Ω in Euclidean space. This note verifies a conjecture of Arcozzi and Björn concerning the completeness of the space of harmonic functions u on Ω that are bounded on E, where the supremum norm is taken with respect to the restriction of u to E.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

References