Abstract Harmonic analysis

Topological groups, locally compact groups, Haar measure. Modular function, convolutions, homogenous spaces , unitary representations, Gelfand-Raikov theorem
Functions of positive type, GNS construction, Potrjagin dulaity, Bochner's theorem, Induced representations, Mackey's impritivity theorem.

Books

• G. B. Folland: A course in Abstract Harmonic Analysis. Studies in Advanced mathematics, CRC press, 1995.
• E. Hewitt and K. Ross: Abstract Harmonic Analysis , Vol 1, Springer 1979
• S. A. Gaal. Linear Analysis and Representation theory. Springer