$Lip\alpha$ harmonic approximation on closed sets
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- by A. Bonilla and J. C. Fariña PDF
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Abstract:
In this paper the $Lip\alpha$ harmonic approximation ($0 < \alpha < \frac {1}{2}$) on relatively closed subsets of a domain in the complex plane is characterized under the same conditions given by S. Gardiner for the uniform case. Thus, the result of P. Paramonov on $Lip\alpha$ harmonic polynomial approximation for compact subsets is extended to closed sets. Moreover, the problem of uniform approximation with continuous extension to the boundary for harmonic functions and similar questions in $Lip\alpha$ harmonic approximation are also studied.References
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Additional Information
- A. Bonilla
- Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Canary Islands, Spain
- Email: abonilla@ull.es
- J. C. Fariña
- Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Canary Islands, Spain
- Email: jcfarina@ull.es
- Received by editor(s): January 30, 2000
- Published electronically: February 9, 2001
- Additional Notes: This work was supported in part by Consejería de Educación, Gobierno Autónomo de Canarias, Proyecto PI 1999/105.
- Communicated by: J. Marshall Ash
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2741-2752
- MSC (2000): Primary 31A05; Secondary 30E10
- DOI: https://doi.org/10.1090/S0002-9939-01-05868-3
- MathSciNet review: 1838798