Fourier and Fourier-Stieltjes' series, summability kernels,
convergence tests. Fourier transforms, the Schwartz space, Fourier
Inversion and Plancherel theorem. Maximal functions and
boundedness of Hilbert transform. Paley-Wiener Theorem. Poisson
summation formula, Heisenberg uncertainty Principle, Wiener's Tauberian
theorem. Introduction to wavelets and
multi-resolution analysis.
Suggested Texts :
1. E. M. Stein and R. Shakarchi, Fourier Analysis: An Introduction, Princeton UniversityPress (2003).
2. Y. Katznelson, An introduction to harmonic analysis, Dover Publications (1976).
3. E.M. Stein and G.Weiss, Introduction to Fourier Analysis on Euclidean Spaces,
PrincetonUniversity Press (1971).
4. E. Hernandez and G. Weiss, A first course on wavelets, Studies in Advanced Mathematics.CRC Press (1996).
- Teacher: B Rajeev