Abstract Harmonic Analysis: Structure of topological groups, integration theory, group representations
Contents: Preliminaries. - Elements of the theory of topolo- gical groups. -Integration on locally compact spaces. - In- variant functionals. - Convolutions and group representa- tions. Characters and duality of locally compact Abelian groups. - Appendix: Abelian groups. Topological linear spa- ces. Introduction to normed algebras. - Bibliography. - In- dex of symbols. - Index of authors and terms.
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0-dimensional A-measurable arbitrary Banach algebra cardinal number character group closed subgroup compact Abelian group compact elements compact set compact subset Consider continuous character continuous homomorphism convolution coset defined Definition dense direct product discrete disjoint easy elements of G finite number follows G contains G is topologically group G Haar integral Haar measure Hausdorff space Hence Hilbert space homomorphism identity implies inequality infinite integer invariant mean left Haar integral left invariant Lemma Let F Let G Let H linear space linear subspace locally compact Abelian locally compact group Ma(G metric nonnegative integer nonvoid nonzero norm normal subgroup obvious open basis open sets open subgroup open subset plainly positive integer positive number Proof properties prove real numbers semigroup sequence subgroup H subgroup of G subset of G Suppose symmetric neighborhood T0 group Theorem topological group topological space topologically isomorphic torsion-free write