MATH 648 Harmonic Analysis on Locally Compact Groups

Topological groups. Theorems of Urysohn's type. Haar integral over a locally compact group, commutative group and its dual. Pontryagin's duality theorem, group algebra. Unitary representation of a group and corresponding representation of group algebra. Stone's theorem. Positive definite functions and Bochner's theorem. Applications of Gelfand's theory to the group algebra. Prerequisite: 646.