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The Mean-value of Meromorphic Functions with Respect to a Generalized Boolean Transformation

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Abstract

A formula for the mean-value distribution of certain meromorphic functions on a vertical line s = σ+iℝ under a generalized Boolean transformation, called rational Boolean transformation from ℝ into itself, is derived using Birkhoff’s ergodic theorem. This formula is represented as a computable integral. Using the Cauchy’s integral theorem, values of this integral corresponding to various possible cases are explicitly computed.

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Acknowledgements

The authors would like to express their deepest gratitude to Prof. Jörn Steuding, Prof. Vichian Laohakosol for valuable remarks and corrections to a previous version. Moreover, the authors would like to thank the owners of the references mentioned in this paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok, 10900, Thailand

    Nattiwut Maugmai & Teerapat Srichan

Authors
  1. Nattiwut Maugmai
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  2. Teerapat Srichan
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Correspondence to Teerapat Srichan.

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The second author is supported by Thailand research fund (Grant No. MRG6080210)

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Maugmai, N., Srichan, T. The Mean-value of Meromorphic Functions with Respect to a Generalized Boolean Transformation. Acta. Math. Sin.-English Ser. 35, 662–670 (2019). https://doi.org/10.1007/s10114-019-8218-7

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  • DOI: https://doi.org/10.1007/s10114-019-8218-7

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