Distributional fractional powers of similar operators. Applications to the Bessel operators

Abstract

This paper provides a method to study the non-negativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and non-negative, we can study the complex powers using an appropriate locally convex space. In this case, the initial operator also will be non-negative and we will be able to study their powers. In particular, we have applied this method to Bessel-type operators.