## Farrell sets for harmonic functions

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- by Stephen J. Gardiner and Mary Hanley PDF
- Proc. Amer. Math. Soc.
**131**(2003), 773-779 Request permission

## Abstract:

Let $F$ denote a relatively closed subset of the unit ball $B$ of $\mathbb {R} ^{n}$. The purpose of this paper is to characterize those sets $F$ which have the following property: any harmonic function $h$ on $B$ which satisfies $\left | h\right | \leq M$ on $F$ (where $M>0$) can be locally uniformly approximated on $B$ by a sequence of harmonic polynomials which satisfy the same inequality on $F$. This answers a question posed by Stray, who had earlier solved the corresponding problem for holomorphic functions on the unit disc.## References

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## Additional Information

**Stephen J. Gardiner**- Affiliation: Department of Mathematics, University College Dublin, Dublin 4, Ireland
- MR Author ID: 71385
- ORCID: 0000-0002-4207-8370
- Email: stephen.gardiner@ucd.ie
**Mary Hanley**- Affiliation: Department of Mathematics, University College Dublin, Dublin 4, Ireland
- Email: mary.hanley@ucd.ie
- 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
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1937416