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Isolated Singularities of Harmonic Functions

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Modern Developments in Multivariate Approximation

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 145))

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Abstract

The main result of this paper gives a sufficient condition for removability of an isolated singularity of a harmonic function. The condition is given in terms of Newtonian capacity. In addition, an application to an approximation problem is presented.

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References

  1. C. A. Berenstein, R. Gay: Complex Variables, Springer, New York, 1997.

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  2. W. K. Hayman, L. Karp, H. S. Shapiro: Newtonian capacity and quasi balayage, Rend. Mat. Appl. 20, no. 7 (2000), 93–129.

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  3. U. Kuran: n—Dimensional extensions of theorems on conjugate functions, Proc. London Math. Soc. 15, no. 3 (1965), 713–730.

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Author information

Authors and Affiliations

  1. Department of Mathematics, ORT Braude College, P.O. Box 78, Karmiel, 21982, Israel

    Lavi Karp

  2. Department of Mathematics, Royal Institue of Technology, S-100 44, Stockholm, Sweden

    Harold S. Shapiro

Authors
  1. Lavi Karp
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  2. Harold S. Shapiro
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Editor information

Editors and Affiliations

  1. Mathematisches Institut, Gerhard-Mercator-Universität Duisburg, 47048, Duisburg, Germany

    Werner Haussmann

  2. Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, 70593, Stuttgart, Germany

    Kurt Jetter

  3. Fachbereich Mathematik, Universität Dortmund, 44221, Dortmund, Germany

    Manfred Reimer  & Joachim Stöckler  & 

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© 2003 Springer Basel AG

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Karp, L., Shapiro, H.S. (2003). Isolated Singularities of Harmonic Functions. In: Haussmann, W., Jetter, K., Reimer, M., Stöckler, J. (eds) Modern Developments in Multivariate Approximation. International Series of Numerical Mathematics, vol 145. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8067-1_9

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  • DOI: https://doi.org/10.1007/978-3-0348-8067-1_9

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9427-2

  • Online ISBN: 978-3-0348-8067-1

  • eBook Packages: Springer Book Archive

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