# Course

## M555 - Harmonic Analysis

Course No:
M555
Credit:
4
Prerequisites:
M301
Approval:
2014
UG-Elective
Syllabus:
Fourier series and its convergences, Dirichlet kernel, Frejer kernel, Parseval formula and its applications. Fourier transforms,the Schwartz space, Distribution and tempered distribution, Fourier Inversion and Plancherel theorem. Fourier analysis on $L_p$ -spaces. Maximal functions and boundedness of Hilbert transform. Paley-Wiener Theorem for distribution. Poisson summation formula, Heisenberg uncertainty Principle, Wiener’s Tauberian theorem.
Reference Books:
1. Y. Katznelson, “An Introduction to Harmonic Analysis”, Cambridge University Press, 2004.
2. E. M. Stein, G. Weiss, “Introduction to Fourier Analysis on Euclidean Spaces”, Princeton Mathematical Series 32, Princeton University Press, 1971.
3. G. B. Folland, “Fourier Analysis and its Applications”, Pure and Applied Undergraduate Texts 4, America Mathematical Society, 2010.