Integrated MSc-PhD Program


KSM4E10: Harmonic Analysis

Topics covered include topological groups, locally compact groups, Haar measure, modular function, convolutions, homogeneous spaces, unitary representations, Gelfand-Raikov Theorem, functions of positive type, GNS construction, Pontryagin duality, Bochner’s theorem, induced representations, and Mackey’s imprimitivity theorem.

Suggested texts:

          1. Folland, G. B., A Course in Abstract Harmonic Analysis, Studies in Advanced Mathematics, CRC Press, 1995.
          2. Hewitt, E. and Ross, K., Abstract Harmonic Analysis, Vol. 1, Springer, 1979.
          3. Gaal, S.A., Linear Analysis and Representation Theory, Dover, 2010.