MA746: Fourier Analysis, during July-Nov 2025

 Preamble: This course offers a rigorous introduction to Fourier Analysis, a foundational area with deep connections across pure and applied mathematics. Beginning with orthogonal systems and Fourier series, the course develops a comprehensive understanding of convergence properties, L^2 theory, and inversion techniques. Emphasis is placed on both classical results and modern applications, including connections with complex analysis, distribution theory, and solutions to boundary value problems. Advanced topics such as Paley-Wiener and Tauberian theorems, Bessel functions and orthogonal polynomials are also explored.

 Syllabus: Orthogonal systems, Trigonometric system, Fourier series in these systems, Uniqueness and convergence, Fourier series of continuous and smooth functions, $L^2$ theory of Fourier series - inversion formula and the Parseval identity, Fourier analysis and complex function theory, Paley Wiener's theorem, Tauberian theorem, Dirichlet problem, Bessel functions, Orthogonal polynomials, Fourier analysis and filters, Fourier transforms and distributions.

Texts/References:
1. I.H. Dym, and H.P. Mc Kean, Fourier Series and Integrals, Academic Press, 1985.
2. G.B. Folland , Fourier Analysis and Applications, Brooks/ Cole Mathematics Series, 1972.
3. Y. Katznelson, An Introduction to Harmonic Analysis, Dover, New York, 1976.
4. T. Korner, Fourier Analysis, Cambridge, 1989.
5. W. Rudin, Functional Analysis, Tata Mc. Graw Hill, 1974.

Course policy (click here)

Classroom and slot: 2203, Slot-C (Mon 10:00 -10:55, Tues 11:00 -11:55, Thu 08:00 08:55, Fri 09:00 -09:55)


Lecture Notes:  Note that this course closely resembles MA746 (Fourier Analysis, 2019). For reference, you may consult the previous course materials available at: https://fac.iitg.ac.in/rksri/MA746_2019.htm

Assignments: Assignment 1

Exams:

Class Discipline:

Students must ensure that mobile phones are switched off or set to silent mode and kept securely inside their bags, which must remain under the desk throughout the class. Only a notebook and a pen are permitted on the desk - no other items are allowed. Any student found with a mobile phone or any electronic device on the desk, regardless of intent, will be required to leave the classroom immediately and the incident will be reported to the Academic Section without exception.