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Counterexamples to Bicomplex Analogue of Bloch’s Principle and its Converse

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Abstract

In this paper, counterexamples to the bicomplex analogue of Bloch’s principle and its converse are given.

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Notes

  1. There are different notations for the set of bicomplex numbers, like \(\mathbb {C}_2, \mathbb {T}, \mathbb {B}\mathbb {C}\) etc. We fix it to be \(\mathbb {B}_{\mathbb {C}}\) more indicative towards the pairs of complex numbers.

  2. \(\Omega \) admits compact exhaustion (see [14, Proposition 4.76])

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Acknowledgements

The authors express their deep gratitude to the anonymous reviewer for his/her valuable comments and remarks which have enhanced the quality of the paper.

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Correspondence to Shivani Pandita.

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Communicated by Irene Sabadini

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This article is part of topical collection in “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.

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Charak, K.S., Pandita, S. & Sharma, N. Counterexamples to Bicomplex Analogue of Bloch’s Principle and its Converse. Complex Anal. Oper. Theory 17, 73 (2023). https://doi.org/10.1007/s11785-023-01380-6

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