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We obtain a set of generalized eigenvectors that provides a generalizedspectral decomposition for a given unitary representation of a commutative,locally compact topological group. These generalized eigenvectors arefunctionals belonging to the dual space of a rigging on the space of squareintegrable functions on the character group. These riggings are obtainedthrough suitable spectral measure spaces.

Riggings of locally compact abelian groups