Abstract
We obtain a new representation of potential and flow functions for spatial potential solenoidal fields with axial symmetry. We study principal algebraic-analytic 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I.P. Mel’nichenko and S. A. Plaksa, “Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. I,”Ukr. Mat. Zh.,41, No. 11, 1518–1529 (1996).
M. A. Lavrent’ev and B. V. Shabat,Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow 1987.
Rights and permissions
About this article
Cite this article
Mel’nichenko, I.P., Plaksa, S.A. Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. II. Ukr Math J 48, 1916–1926 (1996). https://doi.org/10.1007/BF02375377
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02375377