Harmonic analysis on Grassmannian bundles

Strichartz, Robert S.

doi:10.1090/S0002-9947-1986-0837819-6

Harmonic analysis on Grassmannian bundles
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by Robert S. Strichartz PDF

Trans. Amer. Math. Soc. 296 (1986), 387-409 Request permission

Abstract:

The harmonic analysis of the Grassmannian bundle of $k$-dimensional affine subspaces of ${{\mathbf {R}}^n}$, as a homogeneous space of the Euclidean motion group, is given explicitly. This is used to obtain the diagonalization of various generalizations of the Radon transform between such bundles. In abstract form, the same technique gives the Plancherel formula for any unitary representation of a semidirect product $G \times V$ ($V$ a normal abelian subgroup) induced from an irreducible unitary representation of a subgroup of the form $H \times W$.

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