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On Vekua Systems and Their Connections to Hyperbolic Function Theory in the Plane

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Abstract

In this paper we study the solutions of the equation

$$\Delta w- \frac{\alpha}{y}\partial_{y}w = 0,$$

where w is a complex valued function. This equation is related to the generalized axially symmetric potential theory which has been studied notably by Weinstein, see [12]. We have researched this equation earlier in higher dimensions in connection with the hyperbolic function theory. In this paper will see how this equation is related to the generalized analytic functions in the hyperbolic upper half-plane. We also study harmonic differential forms in the hyperbolic plane and using these we obtain special type of solutions for the preceding equation.

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Authors and Affiliations

  1. Korkeakoulunkatu 10, 33720, Tampere, Finland

    Sirkka-Liisa Eriksson & Heikki Orelma

Authors
  1. Sirkka-Liisa Eriksson
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  2. Heikki Orelma
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Correspondence to Sirkka-Liisa Eriksson.

Additional information

To Professor Klaus Gürlebeck on the occasion of his 60th birthday in October 2014.

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Eriksson, SL., Orelma, H. On Vekua Systems and Their Connections to Hyperbolic Function Theory in the Plane. Adv. Appl. Clifford Algebras 24, 1027–1038 (2014). https://doi.org/10.1007/s00006-014-0507-8

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  • DOI: https://doi.org/10.1007/s00006-014-0507-8

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