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)


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


Harmonic Function Maximum Principle Open Ball Homogeneous Polynomial Independent Interest 
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  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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