** M3/4P18 Fourier Analysis and Theory of Distributions 2018**

Ari Laptev

**Course information
**

The main goal of this course is to give an introduction to basic facts of Theory Distributions.

Office hour: Mondays 12:00-13:00

Content

- Spaces of test functions and distributions.
- Fourier Transform.
- Poisson's summation formula
- Convolutions of distributions.
- Fundamental solutions
- Paley-Wiener Theorem
- Wavefront set
- Wave group for Harmonic oscillator
- Stationary phase method
- Basic Sobolev Inequalities, Sobolev spaces.

Lectures

Lectures - week 2

Course Works

Enhanced Course Work

**Books**

** Lars Hoermander, **
* The Analysis of Linear Partial Differential Operators v.I
Distribution Theory and Fourier Analysis*
Springer, Second Edition 1990.

**Other books**

**M. Reed and B. Simon,**
* Methods of modern mathematical physics. I. Functional Analysis, *
Academic Press, 1980.