EHU Reading Course 2026 - Introduction to Fourier Analysis
EHU Reading Course 2026 - Introduction to Fourier Analysis
This reading course will serve as an introduction to Fourier Analysis aimed at students with a background in real and complex analysis, and lectures will be coordinated by
Mateus Sousa (BCAM Ramón y Cajal Fellow)
Daniel Eceizabarrena (BCAM Ramón y Cajal Fellow)
The course will be roughly divided into 3 parts:
I. The periodic setting (Fourier series);
II. The Euclidian setting (Fourier transform);
III. The finite group setting (Characters and the Fast Fourier transform).
The course will take place on classroom 0.12 of EHU Faculty of Sciences in Leioa, and will start on February 4th, 2026. The plan is to have a total of 13 sessions, divided into 10 lectures of 1h30 and 3 days for student presentations. Student presentations will take place right after the last lectures of each part, and the distribution of topics will be done at the beginning of February.
The isoperimetric inequality.
Weyl's equidistribution theorem
The Riemann and Weierstrass functions
The Schrödinger evolution
The Riemann zeta function
Lattices and geometry of numbers
Primes in Arithmetic progression (3 parts)
The course will follow roughly the contents presented in
E. Stein, and R. Shakarchi - Fourier Analysis: An Introduction. Princeton University Press, Princeton, NJ 2003.
Of course there are many other great references one can follow, such as:
J. Duoandikoetxea - Fourier Analysis. Graduate Studies in Mathematics, 29, AMS, Providence, RI 2001.
L. Grafakos - Classical Fourier Analysis. Graduate Texts in Mathematics, 249, Springer, New York, NY 2014.
C. Muscalu, and W. Schlag - Classical and Multilinear Harmonic Analysis. Cambridge University Press, New York, NY 2013.
T. Wolff - Lectures on Harmonic Analysis. American Mathematical Society, Providence, RI 2003.
TBA