Scattering theory for unitary operators

Goals of the Course

In this course, we shall develop the scattering theory for unitary operators, mimicking the better developed theory for self-adjoint operators. The time dependent and time independent approach will be studied, and stationary expressions for the main objects of scattering theory will be constructed. With this subject, we shall also pay tribute to the seminal work of Kato and Kuroda on scattering theory.

Objectives of the Course

Understand the role of scattering theory as a comparison theory and develop the necessary tools for applying this theory in various contexts (from dynamical systems to group representations).

Course Content

0. Motivation
1. Hilbert space and linear operators
2. Spectral for unitary operators
3. Scattering theory
4. Scattering operator

Course Prerequisites

Knowledge on standard undergraduate linear algebra, calculus and advanced calculus.

Related Courses

Any courses on functional analysis.

Course Evaluation Method and Criteria

Grades based on attendance and on written reports. An active participation of the students is expected.

Textbook

Lecture Notes

Additional information

Webpage

Conditions of Other department student's attendance

This course is open for any students at Nagoya University. Motivated undergraduate students are also welcome.

This lecture is provided under Creative Commons Attribution-Non Commercial-ShareAlike 4.0 International.