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16:640:508 - Functional Analysis II

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.

 

Schedule of Sections:

 16:640:508 Schedule of Classes

 

Previous Semesters: