MATH 612 - CLASSICAL HARMONIC ANALYSIS
Prof. Karin Reinhold
ES 153 MWF 11:30 - 12:35
Office Hours: open door.
- An introduction to Harmonic Analysis, Y. Katznelson
- Real variable methods in Harmonic Analysis, A. Torchinsky
- Lectures in Harmonic Analysis, T. Wolff
- A panorama of Harmonic Analysis, S. Krantz
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.
Your grade for the course will be based on 2 in class exams, plus
Exam 1: Oct 1
Exam 2: Nov 5
Exam 4: Dec. 5 (end of presentations)
Last day of classes: Dec 8