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Chapter I Integral Geometry and Radon Transforms
Chapter II Invariant Differential Operators
Chapter III Invariants and Harmonic Polynomials
Chapter IV Spherical Functions and Spherical Transforms
Chapter V Analysis on Compact Symmetric Spaces
analytic arbitrary bijection Cartan Chapter coefficients commutative consider constant converges coordinate Corollary corresponding decomposition defined denote the set differential operator DK(G eigenfunction eigenspace element equation Euclidean finite finite-dimensional fixed follows Fourier series Fourier transform function f given group G Haar measure Harish-Chandra harmonic Helgason Hence holomorphic homogeneous space hyperplane implies induced integral invariant measure inversion formula irreducible isometry K-finite K-invariant Killing form Laplace–Beltrami operator Laplacian Lemma Let f Let G Lie algebra linear mapping f neighborhood nilpotent normal obtain orbit orthogonal Paley–Wiener theorem polynomial Proposition prove radial Radon transform representation of G restriction result Riemannian manifold Riemannian structure roots satisfies semisimple Lie group sinh spherical function spherical transform subalgebra subgroup submanifold subset subspace Suppose surjective symmetric space tion topology totally geodesic vector space Weyl group