Functional Analysis
MAT520 @ Princeton
Description
This is the page for a course at Princeton (fourth in the analysis sequence) taught by the lovely Prof. Jacob Shapiro that I took during Fall 2023. Below is the course description and some resources about the topic.
“Basic introductory course to modern methods of analysis. The possible topics may include $L^p$ spaces, Banach spaces, uniform boundedness principle, closed graph theorem, locally convex spaces, distributions, Fourier transform, Riesz interpolation theorem, Hardy-Littlewood maximal function, Calderon-Zygmund theory, oscillatory integrals, almost orthogonality, Sobolev spaces, restriction theorems, spectral theory of compact operators, applications to partial differential equations.”
We actually went much more toward the spectral theory and the functional calculus direction, and eventually culminated in unbounded operators. One of my favorite courses at Princeton!
Reading List
- Prof. Shapiro’s course page
- Reed & Simon’s Methods of Modern Mathematical Physics I (affectionately “R&S”)
- Walter Rudin’s Functional Analysis (aka “Rudin”)
- Jaksic’s “Topics in Spectral Theory”
- Helein’s notes on the spectral theory from Universite Paris Diderot
- Erdman’s notes on operator algebras
- Dana P. Williams’ (very) short course on C* algebras
- Teschl’s Mathematical Methods in Quantum Mechanics textbook (with applications to Schrodinger operators)