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Determining the image of some singular function

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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.

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Authors and Affiliations

  1. Pomeranian Academy in Slupsk, Institute of Mathematics, Slupsk, Poland

    S. Ponomarev

  2. Institute of Mathematics, University of Gdansk, Gdansk, Poland

    A. Gospodarczyk

Authors
  1. S. Ponomarev
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  2. A. Gospodarczyk
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Correspondence to S. Ponomarev.

Additional information

Original Russian Text Copyright © 2013 Ponomarev S. and Gospodarczyk A.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 3, pp. 689–699, May–June, 2013.

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Ponomarev, S., Gospodarczyk, A. Determining the image of some singular function. Sib Math J 54, 545–554 (2013). https://doi.org/10.1134/S003744661303018X

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  • DOI: https://doi.org/10.1134/S003744661303018X

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