An alternative point of view to the theory of fractional Fourier transform

The concept of the fractional Fourier transform is framed within the context of quantum evolution operators. This point of view yields an extension of the above concept and greatly simplifies the underlying operational algebra. It is also proved that a multidimensional extension can be performed by using a biorthogonal multiindex harmonic oscillator basis. It is finally shown that most of the proposed physical interpretations of the fractional Fourier transform are just trivial consequences of the analysis developed in this paper.