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Class R of Gonchar in \(\mathbf C^n\)

  • Azimbay Sadullaev
  • Zafar Ibragimov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 264)

Abstract

The class R in the complex space \({\mathbf C}^{n} \) was introduced and investigated by A. A. Gonchar. This class and its properties have found a number of applications in approximation theory, in problems of analytic continuations of functions, in descriptions of the structures of singular sets of analytic functions, and in pluripotential theory. In this paper we study further properties of this class.

Keywords

Rational approximation Pluripolar set Fine-analytic function Fine topolgy Plurisubharmonic function 

Notes

Acknowledgements

I would like to express my warm thanks to the referee of this paper for numerous corrections, in particular for the wonderful Remark 1.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsNational University of UzbekistanTashkentUzbekistan
  2. 2.Department of MathematicsUrgench State UniversityKhorezm, UrgenchUzbekistan

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