Abstract
We obtain new representations of the potential and flow function of three-dimensional potential solenoidal fields with axial symmetry, study principal algebraic analytic properties of monogenic functions of vector variables with values in an infinite-dimensional Banach algebra of even Fourier series, and establish the relationship between these functions and the axially symmetric potential or the Stokes flow function. The developed approach to the description of the indicated fields is an analog of the method of analytic functions in the complex plane used for the description of two-dimensional potential fields.
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Additional information
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol 49, No. 2, pp. 228–243, February, 1997.
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Mel’nichenko, I.P., Plaksa, S.A. Potential fields with axial symmetry and algebras of monogenic functions of vector variables. III. Ukr Math J 49, 253–268 (1997). https://doi.org/10.1007/BF02486440
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DOI: https://doi.org/10.1007/BF02486440