wigner_D_matrix about s2cnn

[tscohen]

The Wigner D Matrices are to SO(3) what the complex exponentials exp(i n phi) or sinusoids sin(n phi), cos(n phi) are to SO(2). Each entry of a D matrix is a function on SO(3). Likewise, a complex exponential is a function on SO(2). The standard Fourier transform amounts to projecting a function onto a basis of complex exponentials. The SO(3) Fourier transform amounts to projecting a function onto a basis of matrix elements of Wigner D matrices. In both cases, there is a Fourier convolution theorem that says you can perform convolution in the Fourier domain by pointwise (scalar or matrix) multiplication. For more information, see the section on generalized Fourier transforms in our paper, and the references therein.