Introduction to microlocal analysis: 18.157 (`Spring' 2000)

• General information

  Here is a description of the intended course Announcement.
  If you want to print it out, here it is as a postscript file announce.ps.

• Lectures

  
  Lectures are in 2-255, Tuesdays and Thursdays 1-2:30PM. Also there are some additional (optional) lectures on Mondays, 5-6PM, in the same room.
  1. 1st February, 2000: Schwartz test functions, tempered distributions, Schwartz representation theorem, Schwartz kernel theorem. Sections 1.1-1.5.
  2. 3rd February, 2000: Fourier transform, Fourier inversion formula. Sections 1.6-1.8.
  3. 8th February, 2000: Symbols, density, products, ellipticity. Sections 2.1.
  4. 10th February, 2000: Pseudodifferential operators, action on Schwartz' space.
  5. 15th February, 2000: Reduction theorem.
  6. 17th February, 2000: Product of pseudodifferential operators.
  7. 24th February, 2000: Ellipticity, L^2 boundedness started.
  8. 28th February, 2000: L^2 boundedness, Sobolev spaces.
  9. 29th February, 2000: Polyhomogeneity, radial compactification, isotropic algebra.
  10. 2nd March, 2000: Isotropic algebra.
  11. 6th March, 2000: Isotropic composition.
  12. 7th March, 2000: Residual algebra and Fredholm property of isotropic elliptic operators.
  13. 9th March, 2000: The harmonic oscillator.
  14. 13th March, 2000: Traces, determinants and forms.
  15. 14th March, 2000: Fredholm determinant, analytic Fredholm theory.
      Spring hiatus
  16. 13th April, 2000: Reminder and complex order.
  17. 20th April, 2000: index an invertibility.
  18. 24th April, 2000: Fredholm determinant and 1-form.
  19. 25th April, 2000: 2-form and invertibility of families.
  20. 27th April, 2000: Determinant bundle and curvature.

• Lecture Notes

  
  Revised versions of the lecture notes will be provided as I go along.
  • Tempered distributions and the Fourier transform,
    Last revision 3rd February, 2000:
    Chapter1.ps (Postscript):
    Chapter1.dvi (Dvi)
    
  • Pseudodifferential operators on Euclidean space,
    Last revision 6th March, 2000 (from 3rd February, 2000) -- small changes and sections moved into Chapter 3:
    Chapter2.ps (Postscript)
    Chapter2.dvi (Dvi)
    
  • Isotropic and scattering calculi,
    Last revision (Fredholm determinant and alternative sections added) 10 May, 2000:
    Chapter3.ps (Postscript)
    Chapter3.dvi (Dvi)
    
  • Bibliography etc:
    Rear.ps (Postscript)
    Rear.dvi (Dvi)