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

Resumo

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.