Let $T: L^2(\mathbb{R}^n) \rightarrow L^2(\mathbb{R}^n)$ be the Fourier transform. Is there any reasonable definition of fractional Fourier transform (i.e. operator $A$ such that $A^{\alpha}=T$ for $\alpha \in (0,1)$), and if there is, is it of any use?
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closed as no longer relevant by Yemon Choi, S. Carnahan♦, Steve Huntsman, Andy Putman, Harald HancheOlsen Apr 9 '10 at 18:31
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