Properties of Some Extensions of the Quadratic Form of the Vector Laplace Operator

Abstract

We consider the action of the quadratic form of the Laplace operator and its extensions in subspaces of linear combinations of the “transverse” and “longitudinal” functions with the fixed orbital momentum with respect to the coordinate origin. In the statement of the problem, it is required that the extensions obtained, after the transfer back to the space of vector functions, can be represented as simple limit expressions with two coefficients. We study the behavior of these coefficients with respect to the initial choice of the linear subspace. Bibliography: 5 titles.