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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 451, Pages 14–28 (Mi znsl6343)  
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
Full-text PDF (235 kB) Citations (3)
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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.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00535А
Volkswagen Foundation
Received: 01.11.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 226, Issue 6, Pages 701–710
DOI: https://doi.org/10.1007/s10958-017-3559-1
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Bel16}
\by M.~I.~Belishev
\paper On algebras of three-dimensional quaternionic harmonic fields
\inbook Mathematical problems in the theory of wave propagation. Part~46
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 451
\pages 14--28
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6343}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3589164}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 226
\issue 6
\pages 701--710
\crossref{https://doi.org/10.1007/s10958-017-3559-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85030321272}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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