Course Archives Theoretical Statistics and Mathematics Unit
Course: Fourier Analysis
Time: Currently not offered
Level: Postgraduate
Syllabus
Past Exams


Syllabus: 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).

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Past Exams
Midterm
05.pdf 06.pdf 09.pdf 11.pdf 13.pdf 15.pdf 17.pdf
Solutions
13.pdf 15.pdf
Semestral
05.pdf 06.pdf 09.pdf 11.pdf 13.pdf 15.pdf 17.pdf
Solutions
13.pdf 15.pdf
Supplementary and Back Paper
15.pdf 17.pdf

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