| Week | Tuesday | Thursday |
|---|---|---|
| 1 |
Apr 2: LCH spaces (4.5); Positive linear functionals, Construction of Radon measures (7.1) | Apr 4: Riesz representation for positive linear functionals (7.1) |
| 2 |
Apr 9: Inner and outer approximation, Density of Cc(X) in Lp, Lusin's theorem (7.2) | Apr 11: Jordan decomposition of real linear functionals, Riesz representation theorem for complex measures (7.3) |
| 3 |
Apr 16: Review of complex Borel measures (Ch 3) | Apr 18: Weak topologies, Frechet spaces, Alaoglu's Theorem (4.6, 5.4) |
| 4 |
Apr 23: Semicontinuity, LSC and USC approximations (7.2) | Apr 25: Weak derivatives of BV functions, cumulative distributions and FTC for Borel measures (3.5, notes) |
| 5 |
Apr 30: Uniform convexity (notes); convolutions (8.2) | May 2: Schwartz space (8.1); Intro to Fourier transform (8.3) |
| 6 |
May 7: Intro to Fourier transform (8.3); approximate identities (8.2, notes) | May 9: Pointwise convergence of Fourier transform (8.4); Tempered distributions (9.2, notes), FT of 1/(x +- i epsilon) |
| 7 |
May 14: More on tempered distributions (9.2, notes); Sobolev spaces (9.3, notes) | May 16: Sobolev spaces (9.3, notes) |
| 8 |
Monday May 20:
240 Qual time and place TBA |
May 23:
No Class |
| 9 |
May 28: Sobolev spaces (9.3, notes); Dyadic rearrangements (notes) | May 30: HLS inequality; Lp Sobolev embeddings (notes) |
| 10 | Jun 4: Rellich compactness (6.3, notes); Schrodinger ground states (notes) | Jun 6: Schrodinger ground states (notes) |