prerequisite: MA2223 and MA2224
Duration: Micaelmas term, 11 weeks
Number of lectures per week: 3 lectures including tutorials per week
ECTS credits: 5
End-of-year Examination: A 2-hour examination in Trinity term,
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.
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.
Learning Outcomes: On sucessful completion of this module, students will be able to:
compute the Fourier coefficients of a given function;