We obtain a set of generalized eigenvectors that provides a generalized spectral decomposition for a given unitary representation of a commutative, locally compact topological group. These generalized eigenvectors are functionals belonging to the dual space of a rigging on the space of square integrable functions on the character group. These riggings are obtained through suitable spectral measure spaces.
Manuel Gadella. Fernando Gómez. Sujeev Wickramasekara. "Riggings of Locally Compact Abelian Groups." J. Geom. Symmetry Phys. 11 23 - 31, 2008. https://doi.org/10.7546/jgsp-11-2008-23-31