RT7.2. Finite Abelian Groups: Fourier Analysis

Показать описание

Representation Theory: With orthogonality of characters, we have an orthonormal basis of L^2(G). We note the basic philosophy behind the Fourier transform and apply it to the character basis. From this comes the definition of convolution, explored in 7.3.

Рекомендации по теме

Комментарии

The main real world application is trig interpolation polynomials, which are a course unto themselves. The goals of this playlist is to map out the main results for compact groups. Using finite groups, there is no hard analysis, but the story is more or less the same. I'm also interested in motivating Fourier series through group theory.

MathDoctorBob

The trivial example gives the whole game away. After that, it's bookkeeping. I've been posting problems sets with solutions at ureddit. More examples there.

The big questions for here are classifying irreducibles, determining what irreducibles occur in a given representation, and defining projections onto the irreducible subspaces.

MathDoctorBob

is there any practical consequence of this fourier analysis on a finite abelian group? i can image that.

wdlang

i mean the example in your lecture is a bit trivial for me

wdlang

RT7.2. Finite Abelian Groups: Fourier Analysis

RT7.2. Finite Abelian Groups: Fourier Analysis

RT7.1: Finite Abelian Groups: Character Orthogonality

RT7.3. Finite Abelian Groups: Convolution

Fourier analysis on finite abelian groups, Part 2

Fourier analysis on finite abelian groups, Part 1

Math 139 Fourier Analysis Lecture 31: Fourier Analysis on Finite Abelian Groups

Math 139 Fourier Analysis Lecture 32: Fourier Analysis on Finite Abelian Groups

Math 139 Fourier Analysis Lecture 30: FFT ct'd; Fourier Analysis on Finite Abelian Groups

Introduction to additive combinatorics lecture 7.3 -- dual groups and the discrete Fourier transform

What is...finite Fourier analysis?

499.2: Representations of Finite Abelian Groups

Characters of finite abelian groups

Dual group and Fourier transform in G - Analysis, Random Walks and Groups

RT8.2. Finite Groups: Classification of Irreducibles

Lecture 7 - Fourier Analysis on Finite Groups

Group Theory: Finite abelian groups

Math 139 Fourier Analysis Lecture 28: Finite Fourier Analysis

Finite Fourier Analysis | Ritvik Ramanan Radhakrishnan | B.Math, 3rd year

(Lecture 29) Fourier Analysis

A Course on Fourier Analysis | Lecture -1| Prof. E.K Narayanan

Math 139 Fourier Analysis Lecture 29: Finite Fourier Analysis; Fast Fourier Transform

Fourier Series on the Torus

Journey into Number Theory: Chapter 4: Section 1

RT8.1. Schur Orthogonality Relations