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Integral Identities for Polyanalytic Functions

  • Anastasiia MinenkovaEmail author
  • Olga Trofimenko
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

In this paper we overview some results from the theory of polyanalytic functions. We consider the problem of the mean value of polyanalytic functions of certain types. Similar problems were studied by M.O. Reade, M.B. Balk, and V.V. Volchkov. The cases of polygonal and circular domains with a polynomial weight are studied. We consider the results that are versions of the classical Cauchy, Morera, and Fedoroff theorems for polyanalitic functions under some conditions.

Notes

Acknowledgements

The study was carried out within the Fundamental Research Programme funded by the Ministry of Education and Science of Ukraine, Project No. 0118U003138. The authors want to thank the referee. We highly appreciate his/her comments and suggestions, which significantly contributed to improving the quality of this publication.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ConnecticutStorrsUSA
  2. 2.Department of MathematicsVasyl’ Stus Donetsk National UniversityVinnytsiaUkraine

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