Abstract Harmonic Analysis: Structure of topological groups, integration theory, group representationsSpringer-Verlag, 1979 - Harmonic analysis |
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a₁ arbitrary Banach algebra Borel cardinal number character group closed subgroup compact Abelian group compact set compact subset Consider continuous character continuous homomorphism coset defined Definition denote dense direct product discrete f₁ finite number follows ƒ ƒ G contains group G H₁ h₂ Haar integral Haar measure Hausdorff space Hence Hilbert space homomorphism identity implies infinite invariant mean left Haar integral left invariant Lemma Let f Let G Let H linear space linear subspace locally compact Abelian locally compact group nonvoid nonzero norm normal subgroup obvious open basis open sets open subgroup open subset operator plainly positive integer positive number Proof prove real numbers semigroup sequence subgroup H subgroup of G subset of G Suppose symmetric neighborhood Theorem topological group topological space topologically isomorphic x₁ y₁ ΕΙ