On Namias's Fractional Fourier Transforms

The objective of this paper is to make rigorous a formal study(Namias, 1980) of fractional powers for the Fourier transform.To make the theory unambiguous, it is found necessary to modifyNamias's fractional operators. Some theorems are then provedfor the modified operators and an operational calculus is developed.Finally, an application to an ordinary differential equationis considered.