International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 37

Some light can be shed on the geometric structure of these rotations by the following simple considerations. Note thatso that (and similarly ) is the identity map. Any eigenvalue of or is therefore a fourth root of unity, i.e. ±1 or , and splits into an orthogonal direct sumwhere (respectively ) acts in each subspace by multiplication by . Orthonormal bases for these subspaces can be constructed from Hermite functions (cf. Section 1.3.2.4.4.2) This method was used by Wiener (1933, pp. 51–71).
References
Wiener, N. (1933). The Fourier Integral and Certain of its Applications. Cambridge University Press. [Reprinted by Dover Publications, New York, 1959.]