RG Analysis and Partial Differential Equations
V4B5 - Real and harmonic analysis (Winter term 2014/2015)
Lecturer:
Prof. Dr. Herbert KochTA:
Gennady UraltsevLectures
- 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:
- 08.10 - 15.10
- 15.10 - 22.10
- 22.10 - 29.10
- 29.10 - 05.11
- 05.11 - 12.11
- 12.11 - 19.11
- 19.11 - 26.11
- 26.11 - 3.12
- 10.12 - 17.12
- 07.01 - 14.01
- 14.01 - 21.01
- 21.01 - 28.01
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
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