Properties of some extensions of the quadratic form of the vector Laplace operator

The action of the quadratic form of the Laplace operator and its extensions is treated in subspaces of linear combinations of the “transverse” and “parallel” functions with fixed orbital momentum with respect to the coordinate origin. The problem is posed in such a way that the resulting extensions, when transferred back to the space of vector functions, represent a simple limiting expressions with two coefficients. We study the behavior of these coefficients with respect to the initial choice of the linear subspace.