Farrell sets for harmonic functions

Authors:
Stephen J. Gardiner and Mary Hanley

Journal:
Proc. Amer. Math. Soc. **131** (2003), 773-779

MSC (2000):
Primary 31B05; Secondary 41A28

DOI:
https://doi.org/10.1090/S0002-9939-02-06776-X

Published electronically:
September 17, 2002

MathSciNet review:
1937416

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote a relatively closed subset of the unit ball of . The purpose of this paper is to characterize those sets which have the following property: any harmonic function on which satisfies on (where ) can be locally uniformly approximated on by a sequence of harmonic polynomials which satisfy the same inequality on . This answers a question posed by Stray, who had earlier solved the corresponding problem for holomorphic functions on the unit disc.

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Additional Information

**Stephen J. Gardiner**

Affiliation:
Department of Mathematics, University College Dublin, Dublin 4, Ireland

Email:
stephen.gardiner@ucd.ie

**Mary Hanley**

Affiliation:
Department of Mathematics, University College Dublin, Dublin 4, Ireland

Email:
mary.hanley@ucd.ie

DOI:
https://doi.org/10.1090/S0002-9939-02-06776-X

Received by editor(s):
April 18, 2001

Received by editor(s) in revised form:
October 10, 2001

Published electronically:
September 17, 2002

Additional Notes:
This research was partially supported by EU Research Training Network HPRN-CT-2000-00116

Communicated by:
Juha M. Heinonen

Article copyright:
© Copyright 2002
American Mathematical Society