MTH406: Fourier analysis

        [Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

• Fourier series of a periodic function, Cesàro and Abel summability.
• Poisson Kernel and Dirichlet problem in the unit disc.
• Pointwise and $L^2$-convergence of Fourier series.
• Some application of Fourier series.
• Fourier transformation on ${\mathbb{R}}$, convolution, Plancherel theorem, inversion formula.
• Weierstrass approximation theorem, Poisson summation formula, Hiesenberg uncertainty principle.
• Fourier transformation on ${\mathbb{R}}^d$.

Additional Topics

• Fourier analysis on finite Abelian group.

Recommended Reading

• E. M. Stein and R. Shakarchi, Fourier Analysis, Princeton University Press (2003).
• Walter Rudin, Real and Complex Analysis, McGraw-Hill International Edition (1987).
• G. B. Folland, Fourier Analysis and Its Applications, American Mathematical Society (1992).
• Anton Deitmar and Siegfried Echterhoff, Principles of Harmonic Analysis, Springer (2009).