Geodesic
Extensions of the quadratic form of the transverse Laplace operator
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 23, Tome 433 (2015), pp. 78-110 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Extensions of the quadratic form of the transverse {Laplace} operator},
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T. A. Bolokhov. Extensions of the quadratic form of the transverse Laplace operator. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 23, Tome 433 (2015), pp. 78-110. http://geodesic.mathdoc.fr/item/ZNSL_2015_433_a4/

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