List of harmonic analysis topics

Short description: none

This is a list of harmonic analysis topics. See also list of Fourier analysis topics and list of Fourier-related transforms, which are more directed towards the classical Fourier series and Fourier transform of mathematical analysis, mathematical physics and engineering.

## Contents

* 1 Fourier analysis
* 1.1 Fourier series
* 1.2 Fourier transform
* 2 Topological groups
* 3 Representation theory
* 4 Fast Fourier transform
* 5 Analysis of unevenly spaced data
* 6 Applications

## Fourier analysis

### Fourier series

* Periodic function
* Trigonometric function
* Trigonometric polynomial
* Exponential sum
* Dirichlet kernel
* Fejér kernel
* Gibbs phenomenon
* Parseval's identity
* Parseval's theorem
* Weyl differintegral
* Generalized Fourier series
* Orthogonal functions
* Orthogonal polynomials
* Empirical orthogonal functions
* Set of uniqueness

### Fourier transform

* Continuous Fourier transform
* Fourier inversion theorem
* Plancherel's theorem
* Convolution
* Convolution theorem
* Positive-definite function
* Poisson summation formula
* Paley-Wiener theorem
* Sobolev space
* Time–frequency representation
* Quantum Fourier transform

## Topological groups

* Topological abelian group
* Haar measure
* Discrete Fourier transform
* Dirichlet character
* Amenable group
* Von Neumann's conjecture
* Pontryagin duality
* Kronecker's theorem on diophantine approximation
* Almost periodic function
* Bohr compactification
* Wiener's tauberian theorem

## Representation theory

Main article: List of representation theory topics

* Representation of a Lie group
* Unitary representation
* Irreducible representation
* Harish-Chandra character
* Restricted representation
* Induced representation
* Peter–Weyl theorem
* Spherical harmonic
* Casimir operator
* Hecke operator
* Stone–von Neumann theorem
* Discrete series representation
* Tempered representation
* Langlands program

## Fast Fourier transform

* Bluestein's FFT algorithm
* Cooley–Tukey FFT algorithm
* Rader's FFT algorithm
* Number-theoretic transform
* Irrational base discrete weighted transform

## Analysis of unevenly spaced data

* Least-squares spectral analysis

## Applications

* FFT multiplication
* Spectral method
* Fourier transform spectroscopy
* Signal analysis
* Analytic signal
* Welch method

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/List of harmonic analysis topics. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=List_of_harmonic_analysis_topics&oldid=184685"