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Representations and duality of compact groups
More about representations of compact groups
Miscellaneous facts about representations
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A-almost everywhere apply approximate unit arbitrary Banach algebra belongs Borel measurable character group closed ideal closed subset compact Abelian group compact subset complex numbers conjugate consider contains converges convolution Corollary cosets countable defined definition denote dense direct sum dual object eigenvalues element equal equivalent finite-dimensional follows Fourier transform functions on G group G Haar measure Hence Hilbert space holds homomorphism identity implies inequality infinite irreducible unitary representations Lemma Let f Let G linear space linear subspace locally compact Abelian locally compact group mapping Math matrix neighborhood nonnegative nonvoid nonzero norm normal subgroup notation obtain obvious one-to-one orthogonal orthonormal basis Plainly Plancherel's theorem positive integer positive number positive-definite functions Proof prove RAAA representation of G representation space sequence shows Sidon set space H spectral set spectral synthesis subgroup of G subset of G Suppose tensor product theorem two-sided ideal unitary representation write zero