Requirements/prerequisites: prerequisite: 221
Duration: Hilary term, 10 weeks

Number of lectures per week: 3 lectures including tutorials per week

Assessment:

End-of-year Examination: This module will be examined jointly with MA342B in a 3-hour examination in Trinity term, except that those taking just one of the two modules will have a 2 hour examination.

Description: Harmonic Analysis is one of the most successful and beautiful areas of mathematics. From its origins in Fourier series, it has expanded in various ways - singular integral operators, complex analysis, group representation theory, operator theory.

Topics:

Fourier Series: Origins. Convergence of Cesaro means. Mean-square convergence.

Pointwise convergence (for smooth classes). Failure of pointwise convergence.

Weyl's equidistribution theorem.

Fourier Transform: Definition, inversion, Plancherel formula.

Feb 26, 2010