Positive definite functions and spectral properties of the Schrödinger operator with point interactions.

The article presents the theory of radial positive definite functions on the study of spectral properties of self-adjoint extensions. It provides the classical Schoenberg theorem of a function and equation wherein its value is thought to be strictly positive definite in an inequality function. Another theorem is provided which is expressed in a nonnegative finite Borel measure, having the Bessel function of order.