OVERVIEW

In this course the fundamental notions relative to abstract harmonic analysis will be presented, namely the basics of  unitary representations of locally compact topological groups, emphasizing the analytic aspects and working on some important examples.

The lectures will be delivered in Italian

AIMS AND CONTENT

LEARNING OUTCOMES

The course aims to provide an introduction to distribution theory and some of its applications

AIMS AND LEARNING OUTCOMES

The objective is to introduce the main analytic problems addressed by representation theory, and to develop general techniques relative to integration on homogeneous spaces

PREREQUISITES

Basic notions of Functional Analysis will be used throughout

TEACHING METHODS

Traditional.

The problems’ sessions consist of a blackboard discussion with the students of the proposed exercises

SYLLABUS/CONTENT

The course is divided into four chapters:

•  Topological groups: integration on the group and on its homogeneous spaces 
• Generalities on unitary rappresentations
• Compact groups
• Induced rappresentations

RECOMMENDED READING/BIBLIOGRAPHY

- G. Folland, An Introduction to Abstract Harmonic Analysis, CRC press.

TEACHERS AND EXAM BOARD

Exam Board

FILIPPO DE MARI CASARETO DAL VERME (President)

ERNESTO DE VITO

GIOVANNI ALBERTI (President Substitute)

FRANCESCA ASTENGO (President Substitute)

ANDREA BRUNO CARBONARO (President Substitute)

LESSONS

LESSONS START

In agreement with the academic calendar, approved by the “Consiglio di Corsi di Studi”

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The final grade is based on the discussions that have taken place during the problem sessions and on the oral examination

Students with certified inabilities or special needs are kindly invited to contact the teacher at the beginning of the course in order to agree on the suitable adjustments that respect both the objectives of the course and the individual needs

ASSESSMENT METHODS

The blackboard discussion of the exercises assigned as homework is voluntary and consists in presenting the arguments used in solving the proposed problems, including the difficulties encountered.

The main purpose of the oral examination is to evaluate the students' ability to apply the theory developed in class to the main examples. In the oral examination, the degree of understandin and the ability to explain and connect the various concepts are evaluated.

Exam schedule