Course - Harmonic Analysis - MA8106
Harmonic Analysis
Lessons are not given in the academic year 2010/2011
About
About the course
Course content
This course is taught every second year, next time Spring 2012, provided there is a suffient number of students attending. If there are not enough students, the course may be offered as a supervised self-study.
The course will treat central concepts and results in modern harmonic analysis, which are developments from classical Fourier analysis. One possible theme may be harmonic analysis related to the study of singular integrals and complex and real methods. Some key concepts are: maximal functions, Calderon-Zygmund decompositions, the Hilbert transform, Littlewood-Paley theory, Hardy spaces, Carleson measures, Cauchy integrals, singular integral operators. The course may also cover a more
abstract direction dealing with generalizations of classical Fourier analysis from the unit circle to locally compact Abelien groups. Key concepts are then Haar measure, convolution, the dual group and Fourier transformation, positive definite functions, the inversion theorem, Plancherel's theorem, Pontryagin's duality theorem, the Bohr compactification.
Learning methods and activities
Lectures, alternatively supervised self-study.
Course materials
Will be announced at the start of the course.
Subject areas
- Mathematics