Christopher E. Heil

• Office Hours: MWF 10:00-11:00 and 11:30-12:00, and by appointment.
  
  
• Course Syllabus
  
  
• General Reading List
• Real Analysis Review
• Banach and Hilbert Spaces Review
• A Basis Theory Primer (Chapter 1 is a review of theorems from functional analysis)
• Notes on Lebesgue measure.
  
  
• Lecture notes on metrics, norms, inner products, and topology (updated 1/18/07).
• Lecture notes on Borel measures on R (updated 3/13/07).
  • Additional notes with details on Radon measures on R (updated 3/13/07).
• Lecture notes on operators and dual spaces (updated 2/5/07).
  • Notes on the dual space of c and c_0 (posted 3/21/07).
• Lecture notes on compact sets and finite-dimensional spaces (revised 2/25/07).
• Lecture notes on quotient and product spaces (revised 2/25/07).
• Lecture notes on the Hahn-Banach Theorem and its consequences (posted 2/26/07).
• Lecture notes on the proof of the Hahn-Banach Theorem (posted 2/26/07).
• Lecture notes on reflexive Banach spaces (posted 3/5/07).
  • Proof that L^p is reflexive (posted 4/2/07).
• Lecture notes on the Baire Category Theorem (posted 3/5/07).
• Lecture notes on the Uniform Boundedness Principle (posted 3/28/07).
• Lecture notes on the Open Mapping and Closed Graph Theorems (posted 4/2/07).
• Lecture notes on weak and weak* convergence (posted 4/3/07).
• Lecture notes on adjoints in Banach spaces (posted 4/6/07}.
  • Notes on adjoints in Hilbert spaces (posted 4/5/07).
• Lecture notes on topological vector spaces (revised 4/9/07).
  • Proof that L^p[0,1] has no nontrivial open convex subsets when p<1 (posted 4/5/07).
• Lecture notes (from Harmonic Analysis) on distributions (posted 4/17/07).
  • Notes on the topology for C_c^\infty (posted 4/18/07).
• Lecture notes on the weak and weak* topologies (posted 4/16/07).
  
  
• Homework 1 (due January 31, 2007).
• Homework 2 (due February 12, 2007).
• Homework 3 (due March 9, 2007). Revised version posted 3/1/07.
• Homework 4 (due April 11, 2007).
• Homework 5 (due April 25, 2007).
  
  
• Exam 1 has been rescheduled for February 19, 2007. You will be allowed to bring one 8.5x11 sheet of notes to the exam (you can write on both sides). Topics will include the material on metrics, norms, inner products, and topology, and the material on operators through examples of operators. Measures may be involved in some aspects of the problems, but the questions will focus on spaces and operators rather than measure theory.
  
  
• Exam 2 has been rescheduled for March 16, 2007. You will be allowed to bring one 8.5x11 sheet of notes to the exam. Topics will include dual spaces, finite-dimensional spaces, quotient and product spaces, and the Hahn-Banach Theorem and its consequences.
  
  
• Our Final Exam is scheduled for Thursday, May 3, 2:50-5:40 p.m. You are allowed to bring one 8.5x11 sheet of notes to the exam (you can write on both sides). In addition to the topics covered on Exam 1 and 2, the topics for the final will include reflexivity, Baire Category, Uniform Boundedness, Closed Graph, weak and weak* convergence, topological vector spaces, and the basic definitions concerning distributions.