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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 451, Pages 14–28
(Mi znsl6343)
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This article is cited in 3 scientific papers (total in 3 papers)
On algebras of three-dimensional quaternionic harmonic fields
M. I. Belishevab a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
Abstract:
A quaternionic field is a pair $p=\{\alpha,u\}$ of function $\alpha$ and vector field $u$ given on a 3d Riemannian maifold $\Omega$ with the boundary. The field is said to be harmonic if $\nabla\alpha=\operatorname{rot}u$ in $\Omega$. The linear space of harmonic fields is not an algebra w.r.t. quaternion multiplication. However, it may contain the commutative algebras, what is the subject of the paper. Possible application of these algebras to the impedance tomography problem is touched on.
Key words and phrases:
quaternion harmonic fields, commutative Banach algebras, reconstruction of manifolds.
Received: 01.11.2016
Citation:
M. I. Belishev, “On algebras of three-dimensional quaternionic harmonic fields”, Mathematical problems in the theory of wave propagation. Part 46, Zap. Nauchn. Sem. POMI, 451, POMI, St. Petersburg, 2016, 14–28; J. Math. Sci. (N. Y.), 226:6 (2017), 701–710
Linking options:
https://www.mathnet.ru/eng/znsl6343 https://www.mathnet.ru/eng/znsl/v451/p14
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Abstract page: | 160 | Full-text PDF : | 59 | References: | 37 |
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