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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 296 (1986), 387-409
  • MSC: Primary 43A85; Secondary 22E30, 53C65
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0837819-6
  • MathSciNet review: 837819