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Polynomial Estimates over Exponential Curves in \(\mathbb C^2\)

  • Shirali Kadyrov
  • Yershat Sapazhanov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 264)

Abstract

For any complex \(\alpha \) with non-zero imaginary part we show that Bernstein-Walsh type inequality holds on the piece of the curve \(\{(e^z,e^{\alpha z}) : z \in \mathbb C\}\). Our result extends a theorem of Coman–Poletsky [6] where they considered real-valued \(\alpha \).

Keywords

Bernstein-Walsh inequality Several complex variables Exponential curves 

Notes

Acknowledgements

The first author would like to thank Dan Coman for a useful discussion.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Suleyman Demirel UniversityKaskelenKazakhstan

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