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 18:31This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question. 

