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

TL;DR

This paper introduces a method to analyze the non-negativity and fractional powers of similar operators, with applications to Bessel operators, enhancing understanding of their spectral properties and complex powers.

Contribution

It develops a new approach to study fractional powers of operators with similar spectral features, specifically applied to Bessel-type operators.

Findings

Established a method for non-negativity transfer between similar operators

Applied the method to Bessel operators to analyze their fractional powers

Provided a framework for studying complex powers in locally convex spaces

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.