Some applications of the spectral theory for the integral transform involving the spectral representation (Q1936453)

Summary: In many previous papers, an integral transform \(\mathcal F_{\gamma, \beta}\) 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 \(\mathcal F_{\gamma, \beta}\). Finally we give an application for the spectral representation of a self-adjoint operator which plays a key role in quantum mechanics.