On Namias's Fractional Fourier Transforms
Adam C. McBrideDepartment of Mathematics, University of StrathclydeLivingstone Tower, Glasgow G1 1XHFiona H. KerrDepartment of Mathematics, University of StrathclydeLivingstone Tower, Glasgow G1 1XH
1987en
ABI
Abstract
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 modify Namias's fractional operators. Some theorems are then proved for the modified operators and an operational calculus is developed. Finally, an application to an ordinary differential equation is considered.
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