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Banach space canonical Cc(G character circle group closed invariant closed subgroup coefficient commutative compact subgroup conjugate continuous functions convergence convolution Corollary countable decomposition defined definition denote dimension discrete series dm(x dual eigenvalue End(H End(V equivalent factor representation finite dimensional representation follows formula function f G-morphism group G Haar measure hence hermitian Hilbert space Hilbert sum Hilbert-Schmidt operator homomorphism implies integral invariant measure invariant subspaces irreducible representation isomorphism isotypical component kernel left regular representation left translations Let G Lie groups locally compact group matrices multiplication neighbourhood Neumann algebra neutral element non-zero orthonormal basis particular Plancherel polynomials Proof Proposition prove regular representation representation of G right regular representation right translates rotation s e G scalar operator scalar product Schur's lemma self-adjoint space H subset tc(s theorem topology uniform norm unimodular unitary irreducible representation unitary representation vector space
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Tomá Kopf, Mario Paschke - 2002 - Journal of Mathematical Physics
Mark J Gotay - 1998 - Arxiv preprint math-ph/9809015
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ANASTASIOS MALLIOS - 2002 - Arxiv preprint math-ph/0207035
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and Brown carefully discusses what is known at this time. The ...
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