# 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

, Volume 4 (1) – Mar 7, 2013
3 pages

/lp/springer-journals/completeness-of-spaces-of-harmonic-functions-under-restricted-supremum-nJqwnHyINK
Publisher
Springer Journals
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

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