Real Analysis II

Department: 
MATH
Course Number: 
6338
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every spring and summer semesters

Topics include L^p, Banach and Hilbert spaces, basic functional analysis.

Prerequisites: 

MATH 4318 or consent of the school

Course Text: 

At the level of Folland, Real Analysis

Topic Outline: 
  • Basics of measure theory
  • L^p spaces: Completeness, Riesz representation and the dual of L^p, Hölder's, Jensen's, and Minkowski's inequalities.
  • Topological spaces, normed vectors spaces, compact spaces and the Tychonoff theorem. Linear functionals, Banach and Hilbert spaces, orthonormal bases and orthogonal projections in Hilbert spaces.
  • Basic theorems of functional analysis, including the Hahn-Banach, Baire Category, and open mapping theorems and the uniform boundedness principle.