MATH 5141: Abstract Harmonic Analysis
Description: Harmonic analysis on various spaces such as Euclidean spaces, and abelian and non-abelian locally compact groups. Pontryagin duality, the Peter-Weyl theorem, various Fourier transforms and connections to unitary representation theory. With a change of content, this course is repeatable to a maximum of six credits.
Prerequisites: MATH 5111.
MATH 5141 - Section 1: Abstract Harmonic Analysis - Fourier Analysis
Description: Harmonic analysis on various spaces such as Euclidean spaces, and abelian and non-abelian locally compact groups. We will use the book A Course in Abstract Harmonic Analysis by Gerald Folland (http://www.amazon.com/Abstract-Harmonic-Analysis-Advanced-Mathematics/dp/0849384907) as the textbook. This is an introduction to Fourier analysis on groups and its connections to unitary representation theory. Some of the topics to be covered include locally compact groups, Haar measure, and unitary representations, going into more details on Fourier analysis on abelian groups (dual groups and Pontryagin duality) and compact groups (the Peter-Weyl Theorem).
Sections: Spring 2015 on Storrs Campus
|14670||5141||001||Lecture||TuTh 11:00:00 AM-12:15:00 PM||MSB315||Gordina, Maria|