Laurent series of holomorphic functions smooth up to the boundary

Abstract

It is shown that the Laurent series of a holomorphic function smooth up to the boundary on a Reinhardt domain in \({\mathbb {C}}^n\) converges unconditionally to the function in the Fréchet topology of the space of functions smooth up to the boundary.

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Acknowledgements

The author would like to thank Debraj Chakrabarti for his valuable suggestions, encouragement and support to this work. The author is grateful to the Department of Mathematics, Central Michigan University for providing research assistantship during this work. Also, many thanks to the referee for valuable feedback and comments.

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Correspondence to Anirban Dawn.

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Dawn, A. Laurent series of holomorphic functions smooth up to the boundary. Complex Anal Synerg 7, 13 (2021). https://doi.org/10.1007/s40627-021-00080-1

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Keywords

  • Laurent series
  • Absolute convergence
  • Unconditional convergence
  • Reinhardt domain