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MA5012 Operator Theory - Sommersemester 2016

Lecturer: Simone Warzel

Exercises: Frank Hofmaier

Time and Location

Lecture: Tue 14:15-15:45 in MI 03.10.011, and Th 12:30-14:00 in MI 03.08.011

Supplements: Th 14:00-15:00

Exercises: Mo 12:15-13:45 in CH26410 Tue 12:15-13:45 in MW 0234 and Wed 12:15-13:45 in MI 00.13.036

News

Exercise classes in the week 16.-20.5. are cancelled due to Pentacost holidays.

The class on July 7 is cancelled.

Oral exams will be taken place during the period July 21-28. Exact schedules were distributed by mail.

Prerequisites

Functional analysis [MA3001], complex analysis [MA2006/MA2008]

Contents

Topics: Banach algebras and their spectral theory; spectral theorem in Hilbert spaces; unbounded operators; semigroups

Summary: The central topic of the lecture will be spectral theory and spectral calculus. This is an indispensable technique for the solution of linear evolution equations which arise in many applications ranging from mathematical physics and biology to engineering. The course will follow a top-down approach to the topic starting from the spectral theory in Banach algebras down to the theory of self-adjoint (possibly unbounded) operators in a Hilbert space. In the course of the lecture, applications of these techniques with an emphasis on the area of mathematical physics will be covered.

Exercise Sheets

Literature

-- SimoneWarzel - 06 Apr 2016