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Spherical Harmonics and Integral Geometry on Projective Spaces

1983
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Transactions of the American Mathematical Society
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The Radon transform R on CP" associates to a point function/(jc) the hyperplane function Rf(H) by integration over the hyperplane H. Il R' is the dual transform, we can invert R'R by a polynomial in the Laplace-Beltrami operator, and verify the formula of Helgason [7] with very simple computations. We view the Radon transform as a G-invariant map between representations of the group of isometries G = U(n + 1) on function spaces attached to CP". Pulling back to a sphere via a suitable Hopf

doi:10.2307/1999378
fatcat:znvsbhurkjczbmx7asejstf53a