This is a list of things named after Joseph Fourier:

Mathematics

Budan–Fourier theorem In mathematics, Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity (mathematics), parity of this number. It was published in 1807 by François Budan de Boislaurent. A similar ...

, see

Budan's theorem In mathematics, Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity of this number. It was published in 1807 by François Budan de Boislaurent. A similar theorem was publishe ...

* Fourier's theorem *

Fourier–Motzkin elimination Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities. It can output real solutions. The algorithm is named after Joseph Fourier who proposed the me ...

* Fourier algebra *

Fourier division Fourier division or cross division is a pencil-and-paper method of division which helps to simplify the process when the divisor has more than two digits. It was invented by Joseph Fourier Jean-Baptiste Joseph Fourier (; ; 21 March 1768 – 16 Ma ...

* Fourier method

Analysis

Fourier analysis In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Josep ...

Fourier series A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or ''p ...

Fourier–Bessel series In mathematics, Fourier–Bessel series is a particular kind of generalized Fourier series (an infinite series expansion on a finite interval) based on Bessel functions. Fourier–Bessel series are used in the solution to partial differential e ...

Fourier sine and cosine series In mathematics, particularly the field of calculus and Fourier analysis, the Fourier sine and cosine series are two mathematical series named after Joseph Fourier. Notation In this article, denotes a real valued function on \mathbb which is pe ...

Generalized Fourier series In mathematical analysis, many generalizations of Fourier series have proved to be useful. They are all special cases of decompositions over an orthonormal basis of an inner product space. Here we consider that of square-integrable functions de ...

**Laplace–Fourier series, see Laplace series ** Fourier–Legendre series *

Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...

(

List of Fourier-related transforms This is a list of linear transformations of function (mathematics), functions related to Fourier analysis. Such transformations Map (mathematics), map a function to a set of coefficients of basis functions, where the basis functions are trigonomet ...

): ***

Discrete-time Fourier transform In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term ''discrete-time'' refers to the ...

(DTFT), the reverse of the Fourier series, a special case of the Z-transform around the unit circle in the complex plane ***

Discrete Fourier transform In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex- ...

(DFT), occasionally called the finite Fourier transform, the Fourier transform of a discrete periodic sequence (yielding discrete periodic frequencies), which can also be thought of as the DTFT of a finite-length sequence evaluated at discrete frequencies *** Fast Fourier transform (FFT), a fast algorithm for computing a Discrete Fourier transform *** Finite Fourier transform *** Fractional Fourier transform (FRFT), a linear transformation generalizing the Fourier transform, used in the area of harmonic analysis **

Fourier–Deligne transform In algebraic geometry, the Fourier–Deligne transform, or ℓ-adic Fourier transform, or geometric Fourier transform, is an operation on objects of the derived category of ''ℓ''-adic sheaves over the affine line. It was introduced by Pierre Deli ...

Fourier–Mukai transform In algebraic geometry, a Fourier–Mukai transform ''Φ'K'' is a functor between derived categories of coherent sheaves D(''X'') → D(''Y'') for schemes ''X'' and ''Y'', which is, in a sense, an integral transform along a kernel object ''K'' � ...

* Fourier inversion theorem **

Fourier integral theorem In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively it may be viewed as the statement that if we know all frequency#Frequency_of_waves, fre ...

In physics and engineering

Fourier's law of heat conduction Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its ''thermal conductivity'', and is denoted . Heat spontaneously flows along a tem ...

* Fourier number (

\text

) (also known as the Fourier modulus), a ratio

\alpha t/d^2

of the rate of heat conduction

\alpha t

to the rate of thermal energy storage

d^2

Fourier optics Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the waveform being considered is regarded as made up of a combination, or '' superposition'', of plane waves. It has some parallels to the Huygens–Fresnel pr ...

Fourier transform spectroscopy Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source, using time-domain or space-domain measurements of the radiation, electromagnetic or not. It ca ...

, a measurement technique whereby spectra are collected based on measurements of the temporal coherence of a radiative source

Other

Joseph Fourier University Joseph Fourier University (UJF, french: Université Joseph Fourier, also known as Grenoble I) was a French university situated in the city of Grenoble and focused on the fields of sciences, technologies and health. It is now part of the Universit ...

* 10101 Fourier

Mathematics

Analysis

In physics and engineering

Other

See also