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A class of analytic pairs of conjugate functions in dimension three

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 arc 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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Submitted on : Tuesday, May 25, 2021 - 10:48:19 AM
Last modification on : Sunday, June 26, 2022 - 3:08:43 AM

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P. Baird, E. Ghandour. A class of analytic pairs of conjugate functions in dimension three. Advances in Geometry, De Gruyter, 2019, 19 (3), pp.421-432. ⟨10.1515/advgeom-2018-0034⟩. ⟨hal-03233957⟩

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