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?
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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