In mathematics, orthogonal functions belong to a function space that is a vector space equipped with a bilinear form. When the function space has an interval...

method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined...

self-orthogonal vectors, in which case perpendicularity is replaced with hyperbolic orthogonality. In the case of function spaces, families of functions are...

self-orthogonal vectors, in which case perpendicularity is replaced with hyperbolic orthogonality. In the case of function spaces, families of functions are...

mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other...

functions are a complete set of orthogonal functions used in solid-state physics. They were introduced by Gregory Wannier in 1937. Wannier functions are...

Resource. Giovanni Sansone (1991). Orthogonal Functions. Dover Publications. pp. 1–2. ISBN 978-0-486-66730-0. "Lp Functions" (PDF). Archived from the original...

Walsh functions form a complete orthogonal set of functions that can be used to represent any discrete function—just like trigonometric functions can be...

longer completely orthogonal functions. But when A(t) and φ(t) are slowly varying functions compared to 2πft, the assumption of orthogonality is a common one...

spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, every function defined on the surface of a sphere can be...

completeness in function libraries, like in the mathematical concept: an orthogonal function set is easy to use as a basis into expanded functions, ensuring...

See the entry on orthogonal polynomials for examples of weighted orthogonal functions. Center of mass Numerical integration Orthogonality Weighted mean Linear...

ultraspherical polynomials C(α) n(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight function (1 − x2)α–1/2. They generalize Legendre...

In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi...

an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. The transformation...

basis functions are also called blending functions, because of their use in interpolation: In this application, a mixture of the basis functions provides...

named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of mathematical properties and numerous...

polynomials are an orthogonal basis for L2(R, w(x) dx) consists in introducing Hermite functions (see below), and in saying that the Hermite functions are an orthonormal...

function into a sum of square integrable orthogonal basis functions. The standard Fourier series uses an orthonormal basis of trigonometric functions...

Component Analysis), Eckart–Young theorem (Harman, 1960), or empirical orthogonal functions (EOF) in meteorological science (Lorenz, 1956), empirical eigenfunction...

In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a type of digital transmission used in digital modulation for encoding digital...

square-integrable functions, spaces of sequences, Sobolev spaces consisting of generalized functions, and Hardy spaces of holomorphic functions. Geometric intuition...

Swiss physicist. He developed a complete set of orthogonal functions known as the Wannier functions which became tools of the trade for solid-state theorists...

1910: he used the result as a tool in his research on series of orthogonal functions. His work remained apparently unnoticed outside Italy, probably due...

the theory of orthogonal functions, Lauricella's theorem provides a condition for checking the closure of a set of orthogonal functions, namely: Theorem...

mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, laureate...

In mathematics, orthogonal coordinates are defined as a set of d coordinates q = ( q 1 , q 2 , … , q d ) {\displaystyle \mathbf {q} =(q^{1},q^{2},\dots...

differintegral Generalized Fourier series Orthogonal functions Orthogonal polynomials Empirical orthogonal functions Set of uniqueness Continuous Fourier transform...

the motion of liquid induced by an applied potential Empirical orthogonal functions, in statistics and signal processing Ethyl orthoformate, an organic...

capacity in such scenarios, alternative sets of orthogonal functions called the quasi-orthogonal functions (QOF), which possess optimal minimax cross correlation...