On the self-fractional Fourier functions

It is shown that a self-fractional Fourier function for an angle where N and M are indivisible integers (N < M), is also a self-fractional Fourier function for angles (j = 1, 2, ...). This allows us to define a self-fractional Fourier function of order M. An eigenvalue of a fractional Fourier operator for angle is equal to , where L is an integer.