Harmonic Analysis on Semi-simple Lie Groups, Volume 2 |
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agree Amer analytic assertion assume Banach space basis Cartan subalgebra central character choose clear compact complex connected consequence consider constant continuous converges Corollary corresponding course defined definition denote differential operator dimensional discussion distribution element equation exists fact finite follows formula function function on G given hand Harish-Chandra hence holomorphic integral invariant irreducible Lemma Let G Lie algebra linear locally mapping Math measure moreover normal notations Note obvious pair g polynomial positive present Proof Proposition prove regular relation relative Remark representation representation of G respectively result Retain roots semi-simple Lie group space spherical function subgroup of G subset suppose Theorem theory transform unique unitary usual whence write zero