## 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