MATH 612 - CLASSICAL HARMONIC ANALYSIS
Prof. Karin Reinhold
ES 153 MWF 11:30 - 12:35
Office Hours: open door.
Texts:
- An introduction to Harmonic Analysis, Y. Katznelson
- Real variable methods in Harmonic Analysis, A. Torchinsky
- Lectures in Harmonic Analysis, T. Wolff
http://www.math.ubc.ca/ilaba/wolff/notes_march2002.pdf
- A panorama of Harmonic Analysis, S. Krantz
Sylabus:
Preliminaries: Hilbert spaces and some elements from functional analysis.
Fourier Series on T: fourier coeficients, summability in norm,
pointwise convergence, summability kernels, norm convergence of partial sums.
Convergence in norn of Fourier Series. Divergence at a point
Fourier Transforms on R^n. Fouriere inversion. Plancharel's Theorem.
The unceratinty principle.
The maximal function, the conjugate function. The Hilbert thransform.
Introduction to wavelets.
Prerequisits: m510A
Your grade for the course will be based on 2 in class exams, plus
topics presentation.
Exam 1: Oct 1
Exam 2: Nov 5
Exam 4: Dec. 5 (end of presentations)
Last day of classes: Dec 8