Spring 2026
Maxime Van de Moortel
Course Description:
The course will cover more advanced topics in Functional Analysis and will include the following topics:
Part I: Functional Analysis for PDEs (Variational and Nonlinear Methods)
- Distributions and Sobolev Spaces
• Linear Variational Problems
• Nonlinear Problems and Fixed-Point Theorems
Part II: Operator Theory and Evolution Problems
- Bounded and Unbounded Operator Theory
• Semigroups of Operators (Hille-Yosida Theory)
• Applications to Evolution Equations
Part III: Harmonic Analysis
- Interpolation Theory
• Littlewood-Paley Theory
• Calderón-Zygmund Theory
Text:
#1. Haim Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. #2. Sergiu Klainerman, Lecture Notes in Analysis
Prerequisites:
507 or 501 and permission of the instructor.
******************************************
Spring 2025
Eric Carlen
Course Description:
This course will be an introduction to methods of functional analysis that are widely used in current research. We will begin with the Hill-Yoshida Theorem on generators of semigroups that solve evolution equations, and shall cover spaces of distributions, some harmonic analysis, and methods of the calculus of variations, all will applications to PDE's, linear and non-linear, of current interest.
Text:
Analysis, 2nd edition, by Lieb and Loss
Prerequisites:
507 or 501 and permission of the instructor. (The course will be accessible to my current 501 students.)
******************************************
Spring 2023
Dennis Kriventsov
Course Description:
The course 502 is a continuation of Fall’s 507.
We will pick up where the course 507 ended. Will do the following:
#1. Followthe the book of Haim Brezis "Functional Analysis, Sobolev Spaces and Partial Differential Equations" starting from where 507 ended (Hill-Yosida Theorem, Sobolev Spaces and the Variational Formulation of Boundary Value Problem, The Heat and the Wave Equation)
#2. Presenting Chapter 1-3 of Louis Nirenberg's Lecture Notes on "Topics in Nonlinear Functional Analysis" (Sard's Theorem, Brouwer Degree, Leray-Schauder Degree and Applications to PDEs, Lyapunov-Schmidt Procedure and nonlinear version+ gluing of approximate solutions into genuine solutions, Morse Lemma, a local bifurcation theorem of Krasnoselski, a global bifurcation theorem of Rabinowitz).
Text:
#1. Haim Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. #2. Louis Nirenberg, Topics in Nonlinear Functional Analysis.
Prerequisites:
507 or permission by instructor
******************************************
Spring 2022
Hector Sussmann
Course Description:
This course will be a continuation of Math 16:640:507 Functional Analysis I. The course will develop the spectral theory of bounded and unbounded (not necessarily compact) self-adjoint operators, Sobolev spaces in N dimensions (with applications to elliptic boundary value problems), and spaces of distributions.
Text:
Functional Analysis, by H. Brezis
Prerequisites:
Math 507
**********************************
Spring 2020
Dennis Kriventsov
Course Description:
This course will be a continuation of Math 16:640:507 Functional Analysis I. The course will develop the spectral theory of bounded and unbounded (not necessarily compact) operators on Hilbert spaces, Sobolev spaces in N dimensions (with applications to elliptic boundary value problems), spaces of distributions, and other topics.
Text:
None
Prerequisites:
16:640:507 or equivalent
Schedule of Sections:
16:640:508 Schedule of Classes