Harmonic Analysis Lecture Notes

Details Harmonic Analysis Lecture Notes Harmonic Analysis Lecture Notes

2009-03-23

arxiv.org/abs/0903.3845v1

Mathematics

Classical Analysis and ODEs

176 pages

Scientific paper

These notes present a first graduate course in harmonic analysis. The first part emphasizes Fourier series, since so many aspects of harmonic analysis arise already in that classical context. The Hilbert transform is treated on the circle, for example, where it is used to prove L^p convergence of Fourier series. Maximal functions and Calderon--Zygmund decompositions are treated in R^d, so that they can be applied again in the second part of the course, where the Fourier transform is studied. The final part of the course treats band limited functions, Poisson summation and uncertainty principles. Distribution functions and interpolation are covered in the Appendices. The references at the beginning of each chapter provide guidance to students who wish to delve more deeply, or roam more widely, in the subject.

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