Boundary value formula for the Cauchy integral on elliptic curve

  • Mukhiddin I. MuminovEmail author
  • A. H. M. Murid


In this paper we consider a Cauchy integral on elliptic curve \(\Gamma \) parameterized by equation \(\eta (t)=a \cos t+ib \sin t, a,b>0\). We drive a formula for the boundary values of the Cauchy integral when integral function is Hölder continuous on \(\Gamma \). Hence we extend Hilbert transform to elliptic curves.


Cauchy integral Boundary value Hilbert transform 

Mathematics Subject Classification

Primary 30E25 30C75 Secondary 45E05 



We thank unknown referee for a careful reading of the first manuscript and useful comments.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi MalaysiaJohor BahruMalaysia
  2. 2.UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Institute for Scientific and Industrial Research (ISIR)Universiti Teknologi MalaysiaJohor BahruMalaysia

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