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Reductive Lie Algebra
Spherical Functions and Differential Equations
7 other sections not shown
Amer analytic function analytic subgroup Cartan subalgebra Cartan subgroup choose clear compact subset complex numbers converges Corollary corresponding defined denote the set differential operator equation finite dimensional finite number follows formula Fourier function on G given Haar measure Harish-Chandra Helgason hence Hilbert space holomorphic function Homc invariant integral irreducible representations Iwasawa decomposition Lemma Let G Lie algebra linear function locally summable mapping Math moreover neighborhood non-zero pair gc Plancherel Plancherel Theorem positive roots present number proof of Theorem Proposition reductive Lie algebra representation of G semi-simple Lie group spherical trace function subalgebra of g subgroup of G subspace suppose supra symmetric spaces TCI Banach representation topology transform unitary representation vector Weyl group whence write x e G zero zonal spherical function