The Sign of a Harmonic Function Near a Zero

  • David H. Armitage
  • Stephen J. Gardiner
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 137)

Abstract

We fix a point x 0 in ℝ n , where n ≥ 2, and define
$$[H: = \left\{ {h:his a harmonic function on some ball centered at {x_0}such that h({x_0}) = 0 and h \equiv /0} \right\}$$
.

Keywords

Harmonic Function Maximum Principle Open Ball Homogeneous Polynomial Independent Interest 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Reference

  1. [1]
    D. H. Armitage, S. J. Gardiner: Best one-sided L 1-approximation by harmonic and subharmonic functions, in: Advances in Mul­tivariate Approximation, W. Haußmann, K. Jetter, M. Reimer (eds.), Wiley-VCH, Berlin 1999, pp. 43–56.Google Scholar

Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • David H. Armitage
    • 1
  • Stephen J. Gardiner
    • 2
  1. 1.Department of Pure MathematicsQueen’s University BelfastBelfastNorthern Ireland
  2. 2.Department of MathematicsUniversity College DublinDublin 4Ireland

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