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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, Volume 32, Issue 1, Pages 3–17
DOI: https://doi.org/10.35634/vm220101
(Mi vuu795)
 

MATHEMATICS

Vector fields with zero flux through circles of fixed radius on $ \mathbb{H}^2$

N. P. Volchkovaa, Vit. V. Volchkovb

a Donetsk National Technical University, ul. Artema, 58, Donetsk, 283000, DPR
b Donetsk National University, ul. Universitetskaya, 24, Donetsk, 283001, DPR
References:
Abstract: A classic property of a periodic function on the real axis is the possibility of its representation by a trigonometric Fourier series. The natural analogue of the periodicity condition in Euclidean space $\mathbb{R}^m$ is the constancy of integrals of a function over all balls (or spheres) of fixed radius. Functions with the indicated property can be expanded in a Fourier series in terms of spherical harmonics whose coefficients are expanded into series in Bessel functions. This fact can be generalized to vector fields in $\mathbb{R}^m$ with zero flux through spheres of fixed radius. In this paper we study vector fields which have zero flux through every circle of fixed radius on the Lobachevskii plane $\mathbb{H}^2$. A description of such fields in the form of series in terms of hypergeometric functions is obtained. These results can be used to solve problems concerning harmonic analysis of vector fields on domains in $\mathbb{H}^2$.
Keywords: vector fields, Lobachevskii plane, zero spherical means, Horn hypergeometric series.
Received: 28.01.2022
Accepted: 07.03.2022
Bibliographic databases:
Document Type: Article
UDC: 517.588
MSC: 53C65, 44A35
Language: Russian
Citation: N. P. Volchkova, Vit. V. Volchkov, “Vector fields with zero flux through circles of fixed radius on $ \mathbb{H}^2$”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:1 (2022), 3–17
Citation in format AMSBIB
\Bibitem{VolVol22}
\by N.~P.~Volchkova, Vit.~V.~Volchkov
\paper Vector fields with zero flux through circles of fixed radius on $ \mathbb{H}^2$
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2022
\vol 32
\issue 1
\pages 3--17
\mathnet{http://mi.mathnet.ru/vuu795}
\crossref{https://doi.org/10.35634/vm220101}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4415766}
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    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    References:39
     
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