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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 434, Pages 32–52 (Mi znsl6139)  
This article is cited in 4 scientific papers (total in 4 papers)

Properties of the $l=1$ radial part of the Laplace operator in a special scalar product

T. A. Bolokhov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (232 kB) Citations (4)
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Abstract: We develop self-adjoint extensions of the $l=1$ radial part of the Laplace operator in a special scalar product. The product arises as the transfer of the plain product from $\mathbb R^3 $ into the set of functions parametrizing one of the two components of the transverse vector field. Similar extensions are treated for the square of the inverse operator of the radial part in question.
Key words and phrases: Laplace operator in spherical coordinates, transverse subspace, vector spherical functions, self-adjoint extensions.
Received: 04.06.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 215, Issue 5, Pages 560–573
DOI: https://doi.org/10.1007/s10958-016-2861-7
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: T. A. Bolokhov, “Properties of the $l=1$ radial part of the Laplace operator in a special scalar product”, Investigations on linear operators and function theory. Part 43, Zap. Nauchn. Sem. POMI, 434, POMI, St. Petersburg, 2015, 32–52; J. Math. Sci. (N. Y.), 215:5 (2016), 560–573
Citation in format AMSBIB
\Bibitem{Bol15}
\by T.~A.~Bolokhov
\paper Properties of the $l=1$ radial part of the Laplace operator in a~special scalar product
\inbook Investigations on linear operators and function theory. Part~43
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 434
\pages 32--52
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6139}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3493697}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 215
\issue 5
\pages 560--573
\crossref{https://doi.org/10.1007/s10958-016-2861-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84965082273}
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  • https://www.mathnet.ru/eng/znsl/v434/p32
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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