V4B5 - Real and harmonic analysis
(Winter term 2014/2015)
Lecturer:
Prof. Dr. Herbert Koch
TA:
Gennady Uraltsev
Lectures
- Mo 14.15-16.00, room 1.008
- We 8.15-10.00, room 1.008
TA groups:
- Fr 16:00-18:00, room 1.007
Exercise Sheets:
Contents:
The course introduces the key concepts of real and harmonic analysis, a
number of important expamples,
and their relation to partial differential equations. Keywords are:
Fourier series: Convergence and examples, boundary values of harmonic
functions,
Maximal function, square functions and singular integrals,
Lebesgue spaces, Hardy space, BMO and Littlewood-Paley theory,
almost orthogonality, uncertainty and Fourier restriction.
Application to PDE.
Notes:
Oral examination
- February 19-20, 2015
- March 30-31, 2015
Literature:
- Muscalu and Schlag: Classical and multilinear harmonic analysis, Vol 1,
Cambridge studies in advanced mathematics 137, 2013
- Grafakos: Classical Fourier Analysis, Springer, Graduate Texts in
Mathematics 249, 2008
