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arXiv · 1707.00122

A class of analytic pairs of conjugate functions in dimension three

Paul Baird·Elsa Ghandour
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Abstract

We exploit an ansatz in order to construct power series expansions for pairs of conjugate functions defined on domains of Euclidean $3$--space. Convergence properties of the resulting series are investigated. Entire solutions which are not harmonic are found as well as a $2$-parameter family of examples which contains the Hopf map.

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Paul Baird, Elsa Ghandour. 2017-07-01. A class of analytic pairs of conjugate functions in dimension three. https://arxiv.org/abs/1707.00122

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