Journal of Mathematical Sciences

, Volume 215, Issue 5, pp 560–573 | Cite as

Properties of the Radial Part of the Laplace Operator for l=1 in a Special Scalar Product


We develop self-adjoint extensions of the radial part of the Laplace operator for l = 1 in a special scalar product. The product arises under the passage of the standard product from ℝ3 to the set of functions parametrizing one of two components of the transverse vector field. Similar extensions are treated for the square of the inverse operator of the radial part in question. Bibliography: 8 titles.


Quadratic Form Scalar Product Laplace Operator Inverse Operator Symmetric Operator 
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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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