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Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. I

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Abstract

We obtain a new representation of potential and flow functions for space potential solenoidal fields with axial symmetry. We study principal algebraic-analytical properties of monogenic functions of a vector variable with values in an infinite-dimensional Banach algebra of even Fourier series and describe the relationship between these functions and the axially symmetric potential and Stokes flow function. The suggested method for the description of the above-mentioned fields is an analog of the method of analytic functions in the complex plane for the description of plane potential fields.

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References

  1. E. T. Whittaker and G. N. Watson,A Course of Modern Analysis, Vol. 2, Cambridge University Press, Cambridge (1927).

    Google Scholar 

  2. L. G. Loitsyanskii,Mechanics of Liquid and Gas [in Russian], Nauka, Moscow 1987.

    Google Scholar 

  3. I. P. Mel’nichenko, “On a method for classification of potential flows with axial symmetry,” in:Contemporary Problems in Realand Complex Analysis [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1984), pp. 98–102.

    Google Scholar 

  4. G. M. Fikhtengol’ts,A Course of Differential and Integral Calculus [in Russian], Vol. 2, Nauka, Moscow (1966).

    Google Scholar 

  5. M. A. Lavrent’ev and B. V. Shabat,Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1987).

    MATH  Google Scholar 

  6. P. P. Zabreiko et al.,Integral Equations [in Russian], Nauka, Moscow 1968.

    Google Scholar 

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Authors
  1. I. P. Mel’nichenko
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  2. S. A. Plaksa
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Mel’nichenko, I.P., Plaksa, S.A. Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. I. Ukr Math J 48, 1717–1730 (1996). https://doi.org/10.1007/BF02529493

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  • DOI: https://doi.org/10.1007/BF02529493

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