International Journal of Functional Analysis, Operator Theory and Applications
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Abstract: Let be the anti-dual space of the Fréchet dense subspace of vectors in the Hilbert space of a unitary representation t of a nilpotent Lie
group G. The representation t is induced by a character c of a connected and simply connected subgroup H
of G. Let be the affine variety of the dual of where and being the orthogonal of h
in A linear injective map W
is constructed between the space of distribution vectors and its disintegration It is also displayed an algebra,
isomorphic to the algebra of invariant differential operators
on and which is “diagonal under W”on The spaces and will also be endowed with topologies
in such a way that W is an isometry.
Keywords and phrases: nilpotent Lie group, unitary representation, direct integral decomposition, induced representation, invariant differential operator.
