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Some properties of a Cauchy type integral in a three-dimensional commutative algebra with one-dimensional radical

  • Roman PukhtaievychEmail author
  • Sergiy Plaksa
Article
  • 13 Downloads

Abstract

In the paper we consider a certain analog of the Cauchy type integral taking values in a three-dimensional commutative algebra over the field of complex numbers with one-dimensional radical. We have established sufficient conditions for the existence of limiting values for such an integral. It is also shown that analogues of Sokhotskii–Plemelj formulas hold.

Keywords

Commutative Banach algebra Monogenic function Cauchy type integral Sokhotskii–Plemelj formulas 

Mathematics Subject Classification

30G35 32A26 32A55 

Notes

Acknowledgements

Pukhtaievych R. is a member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). This research was supported by Fondazione Cassa di Risparmio di Padova e Rovigo (CARIPARO) and partially by Ministry of Education and Science of Ukraine (Project No. 0116U001528).

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics “Tullio Levi-Civita”University of PadovaPaduaItaly
  2. 2.Department of Complex Analysis and Potential TheoryInstitute of Mathematics of the National Academy of Sciences of UkraineKievUkraine

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