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Zap. Nauchn. Sem. POMI, 2015, Volume 433, Pages 78–110
(Mi znsl6128)
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This article is cited in 4 scientific papers (total in 4 papers)
Extensions of the quadratic form of the transverse Laplace operator
T. A. Bolokhov
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
Abstract:
We review the quadratic form of the Laplace operator in spehrical coordinates which acts on the transverse components of vector functions on the $3$-dimensional space. Operators, acting on the parametrizing functions of one of the transverse components with angular momentum 1 and 2, appear to be fourth order symmetric differential operators with deficiency indices (1,1). We develop self-adjoint extensions of these operators and propose correspondent extensions for the initial quadratic form. Eigenfuctions of the extensions in question represent a stable soliton-like solutions of the physical system with the quadratic form being a potential energy.
Key words and phrases:
self-adjoint extensions of symmetric operators, quadratic forms, Laplace operator, transverse subspace.
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English version:
Journal of Mathematical Sciences (New York), 2016, 213:5, 671–693
Bibliographic databases:
 
UDC:
517.9
Received: 11.03.2015
Citation:
T. A. Bolokhov, “Extensions of the quadratic form of the transverse Laplace operator”, Questions of quantum field theory and statistical physics. Part 23, Zap. Nauchn. Sem. POMI, 433, POMI, St. Petersburg, 2015, 78–110; J. Math. Sci. (N. Y.), 213:5 (2016), 671–693
Citation in format AMSBIB
\Bibitem{Bol15}
\by T.~A.~Bolokhov
\paper Extensions of the quadratic form of the transverse Laplace operator
\inbook Questions of quantum field theory and statistical physics. Part~23
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 433
\pages 78--110
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6128}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3493681}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 213
\issue 5
\pages 671--693
\crossref{https://doi.org/10.1007/s10958-016-2731-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84957623938}
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http://mi.mathnet.ru/eng/znsl6128 http://mi.mathnet.ru/eng/znsl/v433/p78
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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T. A. Bolokhov, “Properties of the $l=1$ radial part of the Laplace operator in a special scalar product”, J. Math. Sci. (N. Y.), 215:5 (2016), 560–573
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T. A. Bolokhov, “Properties of some extensions of the quadratic form of the vector Laplace operator”, J. Math. Sci. (N. Y.), 229:5 (2018), 487–496
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T. A. Bolokhov, “Resolvents of selfadjoint extensions of the Laplace operator on the solenoidal subspace”, J. Math. Sci. (N. Y.), 243:6 (2019), 835–840
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T. A. Bolokhov, “Scalar products for the regular analytic vectors of the Laplace operator in the solenoidal subspace”, J. Math. Sci. (N. Y.), 242:5 (2019), 642–650
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