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Siberian Mathematical Journal

, Volume 54, Issue 3, pp 545–554 | Cite as

Determining the image of some singular function

  • S. PonomarevEmail author
  • A. Gospodarczyk
Article
  • 39 Downloads

Abstract

The problem is as follows: How to describe graphically the set T(1)(Γ) where \(T(1)(z) = \int_\Gamma {\tfrac{{d\mu (\zeta )}} {{\zeta - z}}} \) and Γ = Γθ is the Von Koch curve, θ ∈ (0, π/4)? In this paper we give some expression permitting us to compute T θ(1)(z) for each z ∈ Γ to within an arbitrary ɛ > 0. Also we provide an estimate for the error.

Keywords

Von Koch curve natural parametrization quasiconformal mapping pseudo-analytic mapping, Cauchy-type integral 

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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Pomeranian Academy in SlupskInstitute of MathematicsSlupskPoland
  2. 2.Institute of MathematicsUniversity of GdanskGdanskPoland

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