Course Content:


Topological groups and their properties, subgroups, quotient groups, locally compact groups, connected groups, Haar measure (without proof), properties
Computation of Haar measures for classical groups, Convolution, Group algebra and its properties, Approximate identities, Examples for the real line R, and the unit circle T, Representation theory of groups, The representations of Group and Group algebras, Positive definite functions, GNS constructions, C*-algebra of a group, Dual group of abelian groups, Fourier transform, Fourier inversion formula, Plancherel theorem for Abelian groups, Irreducible representations of compact non-abelian groups, Peter-Weyl Theory, Plancherel theory for compact groups.

Text Books: (Include ISBN Numbers)

  1. G. Folland A course in Abstract Harmonic analysis CRC Press. 1994. ISBN-13:978-1-4987-2713-6
  2. Loomis: An introduction to Abstract Harmonic analysis Von Nostrand. 1954.ISBN-13:978-0-486-48123-4

References:

  1. W. Fulton & J. Harris, Representation theory: A first course, Springer - Verlag, 1991, ISBN-10: 0387974954, ISBN-13: 978-0387974958.
  2. H. Helson, Harmonic analysis, 2nd ed., Trim Series, Hindustan Book Agency, 1995.
  3. Y. Katznelson, Introduction to harmonic analysis, Cambridge University Press, 2004 (ISBN: 0521543592, 9780521543590); published in 1968 by John Wiley & sons.
  4. E. Hewitt & K.A. Ross, Abstract harmonic analysis, vol. I, Springer-Verlag, 1963, ISBN-13: 978-1-4419-8638-2.
  5. W. Rudin, Real and complex analysis, 2nd ed., TMH Edition, 1962, ISBN-10:0070619875, ISBN-13: 978-0070619876