• Instructor: Thanos Tzavaras,
  tel: (301)-405-5336
  Email: tzavaras at math.umd.edu
  

• Lecture: Tu-Th 11.00 am - 12.15 pm in Math Building room 1311

  Office hours Tu-Th 12.30 - 1.30 pm in room 3312

• Texts:

  Royden and Fitzpatrick, Real Analysis, forthcoming book ;   (Recommended)

  Notes of Sigurd Angenent on Functional Analysis - click here

• Material to be covered:   Banach Spaces, L^p spaces, Convolutions - Approximation, Distributions, Dual Spaces, Hahn-Banach Theorems, Weak Topologies, Baire Category, Open Mapping theorem, Uniform Boundedness Principle, Bounded Operators, Compact Operators, Spectral Theory in Hilbert Spaces.

  Prerequisite: A first course in Real Analysis - like MATH 630

• Texts on reserve at the Math Library:    
  • K. Yosida, Functional Analysis, Springer
  • H. Brezis, Analyse Fonctionelle: Theorie et Applications, Masson
  • P. Lax, Functional Analysis, Wiley

• Grades:   Homework is assigned in class and listed below. The grade of the course will be based on the completed homework sets.

Homework assignments

A refers to problems asigned from the Lecture Notes of Angenent.
E refers to homework problems assigned in class.



• HW 1: due Sep 29
  On distributions: A4, A5, A11, A13, A17, A21
  On Banach Speces: A25, A28, A30, A31, E1, E2

• HW 2: due Oct 15
  On metric spaces: E3, E4
  On Hahn-Banach: A72, A73, A77
  On function spaces: A35, A36, A37, A41, A42, A43, A46, A47

• HW 3: due Nov 5
  On approximation: E5, A44, A53, A54
  On Sobolev spaces: A55, A56, A57, A58, A61, A62

• HW 4: due Dec 10
  On operators: A101, A102, A108, A112, A117
  On Hilbert spaces: A119, A123, A126, A127, A132