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