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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 447, Pages 5–19 (Mi znsl6290)  
Properties of some extensions of the quadratic form of the vector Laplace operator

T. A. Bolokhov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
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Abstract: The action of the quadratic form of the Laplace operator and its extensions is treated in subspaces of linear combinations of the “transverse” and “parallel” functions with fixed orbital momentum with respect to the coordinate origin. The problem is posed in such a way that the resulting extensions, when transferred back to the space of vector functions, represent a simple limiting expressions with two coefficients. We study the behavior of these coefficients with respect to the initial choice of the linear subspace.
Key words and phrases: Laplace operator in spherical coordinates, transverse and parallel subspaces, vector spherical functions, extensions of the quadratic forms.
Funding agency Grant number
Russian Science Foundation 14-11-00598
Received: 08.06.2016
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 229, Issue 5, Pages 487–496
DOI: https://doi.org/10.1007/s10958-018-3691-6
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: T. A. Bolokhov, “Properties of some extensions of the quadratic form of the vector Laplace operator”, Investigations on linear operators and function theory. Part 44, Zap. Nauchn. Sem. POMI, 447, POMI, St. Petersburg, 2016, 5–19; J. Math. Sci. (N. Y.), 229:5 (2018), 487–496
Citation in format AMSBIB
\Bibitem{Bol16}
\by T.~A.~Bolokhov
\paper Properties of some extensions of the quadratic form of the vector Laplace operator
\inbook Investigations on linear operators and function theory. Part~44
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 447
\pages 5--19
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6290}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3580158}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 229
\issue 5
\pages 487--496
\crossref{https://doi.org/10.1007/s10958-018-3691-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85041510126}
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