## Functional analysis

### Contact Details

Manas Rachh

Arthur K Watson - 109

Email: firstname.lastname (at) yale (dot) edu

Office hours: Mon 10-11am, Thursday 4-5 pm, or by appointment

### Lecture notes and reference material

- Fredholm Theory
- Hahn-Banach theorem (Section 2.3)
- Krein-Milman and extreme subsets
- Spectral theorems (Section 4.3,4.4, Chapter 5)

### Problem sets (best 6 out of 7)

- Problem set 1, Tex file, Solution sketch (Upload date: Jan 22, Due date: Feb 5)
- Problem set 2, Tex file, Solution sketch (Upload date: Feb 5, Due date: Feb 19)
- Problem set 3, Tex file, Solution sketch (Upload date: Feb 19, Due date: Mar 5)
- Problem set 4, Tex File, Solution Sketch (Upload date: Mar 5, Due date: Mar 26)
- Problem set 5, Tex File, Solution Sketch (Upload date: Mar 26, Due date: Apr 9)
- Problem set 6, Tex File, Solution Sketch (Upload date: Apr 9, Due date: Apr 16)
- Problem set 7, Tex File, Solution Sketch (Upload date: Apr 16, Due date: Apr 25)

### Practice problem sets

- Practice problem set 1,
Tex file (Upload date: Jan 29)
- Practice problem set 2,
Tex file (Upload date: Feb 13)
- Practice problem set 3,
Tex file (Upload date: Feb 26)
- Practice problem set 4, Tex file (Upload date: Apr 2)

### Midterm - in class (Mar 7)

### Final (May 6, 2pm - 4pm, tentative)

### Syllabus

The topics covered in this class will include:

- Hilbert spaces/Banach spaces
- Continuous linear functionals
- Weak and weak* Topologies
- Principles of functional analysis
- Some geometric aspects of function spaces
- Bounded linear operators and the spectral theorem
- Fredholm Theory and application to integral equations

I will roughly be following the text:
A course in functional analysis, second edition by John B. Conway

### Grading policy

6 Assignments - 30 pts

Midterm - 30 pts

Final - 40 pts

### Homework policy

Late homework will not be accepted. It is
okay to discuss the homework problems with other
students as long as you list down your collaborators.
I would highly recommend to try the problems yourself
before discussing them with your peers.
You must however write your own solutions!

### Feedback

Please feel free to give any feedback regarding the class or if
you want any particular thing to be covered in class.
You can provide anonymous feedback in the box below.
I will be checking it on a regular
basis and adapting the lectures based on that.