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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Harmonic analysis on Grassmannian bundles


Author: Robert S. Strichartz
Journal: Trans. Amer. Math. Soc. 296 (1986), 387-409
MSC: Primary 43A85; Secondary 22E30, 53C65
MathSciNet review: 837819
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0837819-6
PII: S 0002-9947(1986)0837819-6
Keywords: Grassmannian bundle, induced representation, semidirect product, harmonic analysis, generalized Radon transform, Mackey theory, affine symmetric space, Euclidean motion group, integral geometry
Article copyright: © Copyright 1986 American Mathematical Society