The lecture
notes for Math 545 Harmonic Analysis are now complete (5 January 2009).
Topics
- Topic 1 - Fourier coefficients: basic properties
(Complete - Richard Laugesen and Aleksandra Kwiatkowska)
- Topic 2 - Fourier series: summability in norm
(Complete - Richard Laugesen)
- Topic 3 - Fourier series: summability pointwise, Part A
(Complete - Ping Xu)
- Topic 4 - Fourier coefficients in l1
(Complete - Aleksandra Kwiatkowska)
- Topic 5 - Fourier coefficients in l2
(Complete - Ping Xu)
- Topic 6 - Maximal functions (Complete - Noel DeJarnette)
- Topic 7 - Fourier series: summability pointwise, Part B
(Complete - Richard Laugesen)
- Topic 8 - Fourier series: convergence pointwise
(Complete - Eunmi Kim)
- Topic 9 - Fourier series: convergence in norm via Hilbert
transform (Complete - Kostya Sluttsky)
- Topic 10 - Hilbert transform on L2(T)
(Complete - Kostya Sluttsky)
- Topic 11 - Calderon-Zygmund decompositions
(Complete - Kostya Sluttsky)
- Topic 12 - Hilbert transform on Lp(T)
(Complete - Khang Tran)
- Topic 13 - Applications of interpolation
(Complete - Richard Laugesen)
- Topic 14 - Fourier transforms: basic properties
(Complete - Richard Laugesen)
- Topic 15 - Fourier integrals: summability in norm
(Complete - Richard Laugesen)
- Topic 16 - Fourier transform in L1(Rd),
and Fourier inversion (Complete - Richard Laugesen)
- Topic 17 - Fourier transform in L2(Rd)
(Complete - Richard Laugesen)
- Topic 18 - Fourier integrals: summability pointwise
(Complete - Richard Laugesen)
- Topic 19 - Fourier integrals: norm convergence
(Complete - Richard Laugesen)
- Topic 20 - Hilbert and Riesz transforms on
L2(Rd) (Complete - Richard Laugesen)
- Topic 21 - Hilbert and Riesz transforms on
Lp(Rd) (Complete - Richard Laugesen)
- Topic 22 - Compactly supported Fourier transforms, and the
sampling theorem (Complete - Richard Laugesen)
- Topic 23 - Periodization and Poisson summation (Complete -
Richard Laugesen)
- Topic 24 - Uncertainty principles (Complete - Richard Laugesen)
Appendices
- Appendix A - Minkowski's integral inequality
(Complete - Richard Laugesen)
- Appendix B - Lp norms and the distribution function
(Complete - Richard Laugesen)
- Appendix C - Interpolation (Complete - Eunmi Kim)
These notes rearrange the material slightly from what was presented in class
in Fall 2009: smoothness and decay are now treated in Topic 1, and summability
has been split off into Topic 2. Homogeneous Banach spaces over T have been
removed, and instead Minkowski's integral inequality is used (see Appendix A).
Also, I have swapped the order of Topics 4 and 5.
My sincere thanks go to all of you (credited above) who
TeX-ed up parts of the notes!
- Richard Laugesen
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