Properties of matrix-valued spectral coefficients obtained with the Fourier Transform on a non-Abelian group

When using spectral transforms, particular values or features of the spectral coefficients may give information about the properties of the function being transformed. The present paper shows that this is also the case with Fourier transforms on non-Abelian groups. The fact that then some of the spectral coefficients are matrix-valued adds new possibilities to recognize some structural patterns of the spectrum and associate them to properties of the function.