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Eigenfunctions of the Fourier Transform

An eigenfunction of the Fourier transform operator is a function whose shape is identical to that of its Fourier transform. The Gaussian curve, appropriately scaled, is an example. It is well known that there are infinitely many examples like this. This topic is reviewed in this paper, and many interesting properties of these eigenfunctions are discussed. Also discussed is a simple way to characterize all eigenfunctions of the Fourier transform.