Geodesic
Properties of the $l=1$ radial part of the Laplace operator in a~special scalar product
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 43, Tome 434 (2015), pp. 32-52

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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. 
@article{ZNSL_2015_434_a2,
     author = {T. A. Bolokhov},
     title = {Properties of the $l=1$ radial part of the {Laplace} operator in a~special scalar product},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {32--52},
     publisher = {mathdoc},
     volume = {434},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a2/}
}
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T. A. Bolokhov. Properties of the $l=1$ radial part of the Laplace operator in a~special scalar product. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 43, Tome 434 (2015), pp. 32-52. http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a2/