Communications of the
Korean Mathematical Society CKMS

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

Keywords: fractional Bessel operator, distributional operators, Hankel transform

MSC numbers: Primary 47A60, 26A33, 46F10, 46F12, 46F30