Some Applications of the Spectral Theory for the Integral Transform Involving the Spectral Representation

Abstract EN

In many previous papers, an integral transform ℱγ,β was just considered as a transform on appropriate function spaces.

In this paper we deal with the integral transform as an operator on a function space.

We then apply various operator theories to ℱγ,β.

Finally we give an application for the spectral representation of a self-adjoint operator which plays a key role in quantum mechanics.