** 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
- Wavefront set
- Wave group for Harmonic oscillator
- Stationary phase method
- Basic Sobolev Inequalities, Sobolev spaces.

Lectures

Lectures - week 2

Lectures - week 3

Lectures - week 4

Lectures - week 5

Lectures - week 6

Lectures - week 7

Lectures - week 8-9

Problems:

probl.2 sol.2

probl.3 sol.3

Courseworks:

Solutions CW1

The deadline for the first corsework is

Course work 2

Solutions CW2

The deadline for the second corsework is

**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.