Introduction to microlocal analysis: 18.157 (`Spring' 2000)
Here is a description of the intended course
If you want to print it out, here it is as a postscript file announce.ps.
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.
- 1st February, 2000: Schwartz test functions, tempered distributions, Schwartz representation theorem, Schwartz kernel theorem. Sections 1.1-1.5.
- 3rd February, 2000: Fourier transform, Fourier inversion formula. Sections 1.6-1.8.
- 8th February, 2000: Symbols, density, products, ellipticity. Sections 2.1.
- 10th February, 2000: Pseudodifferential operators, action on Schwartz' space.
- 15th February, 2000: Reduction theorem.
- 17th February, 2000: Product of pseudodifferential operators.
- 24th February, 2000: Ellipticity, L^2 boundedness started.
- 28th February, 2000: L^2 boundedness, Sobolev spaces.
- 29th February, 2000: Polyhomogeneity, radial compactification, isotropic algebra.
- 2nd March, 2000: Isotropic algebra.
- 6th March, 2000: Isotropic composition.
- 7th March, 2000: Residual algebra and Fredholm property of isotropic elliptic operators.
- 9th March, 2000: The harmonic oscillator.
- 13th March, 2000: Traces, determinants and forms.
- 14th March, 2000: Fredholm determinant, analytic Fredholm theory.
- 13th April, 2000: Reminder and complex order.
- 20th April, 2000: index an invertibility.
- 24th April, 2000: Fredholm determinant and 1-form.
- 25th April, 2000: 2-form and invertibility of families.
- 27th April, 2000: Determinant bundle and curvature.
Revised versions of the lecture notes will be provided as I go along.
- Tempered distributions and the Fourier transform,
Last revision 3rd February, 2000:
- Pseudodifferential operators on Euclidean space,
Last revision 6th March, 2000 (from 3rd February, 2000) -- small changes and sections moved into Chapter 3:
- Isotropic and scattering calculi,
Last revision (Fredholm determinant and alternative sections added) 10 May, 2000:
- Bibliography etc: