  Using the integral representations of the solutions of Schr\"odinger
equation, which are the essential ingredients of the Gel'fand-Levitan and
Marchenko integral equations of inverse scattering theory, we obtain a general
theorem on the positivity of some integral transforms, and extend the theorem
of Bochner on Fourier transforms of functions of positive type to more general
transforms. The present study is restricted to the positive half-axis. We then
obtain a theorem on the positivity of Fourier cosine transform of the
phase-shifts.
