eigenfunctions

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• eigenfunctions — n. proper function, characteristic vector in a vector space in which elements are functions (Mathematics) …   English contemporary dictionary

• Spectral theory of ordinary differential equations — In mathematics, the spectral theory of ordinary differential equations is concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation. In his dissertation Hermann Weyl… …   Wikipedia

• Fourier transform — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms The Fourier transform is a mathematical operation that decomposes a function into its constituent… …   Wikipedia

• Sturm-Liouville theory — In mathematics and its applications, a classical Sturm Liouville equation, named after Jacques Charles François Sturm (1803 1855) and Joseph Liouville (1809 1882), is a real second order linear differential equation of the formwhere y is a… …   Wikipedia

• Momentum space — The momentum space or k space associated with a particle is a vector space in which every point {kx,ky,kz} corresponds to a possible value of the momentum vector . Representing a problem in terms of the momenta of the particles involved, rather… …   Wikipedia

• Eigenvalue, eigenvector and eigenspace — In mathematics, given a linear transformation, an Audio|De eigenvector.ogg|eigenvector of that linear transformation is a nonzero vector which, when that transformation is applied to it, changes in length, but not direction. For each eigenvector… …   Wikipedia

• Eigenvalues and eigenvectors — For more specific information regarding the eigenvalues and eigenvectors of matrices, see Eigendecomposition of a matrix. In this shear mapping the red arrow changes direction but the blue arrow does not. Therefore the blue arrow is an… …   Wikipedia

• Hermite polynomials — In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence that arise in probability, such as the Edgeworth series; in combinatorics, as an example of an Appell sequence, obeying the umbral calculus; in numerical… …   Wikipedia

• Eigenfunction — [ vibrating drum problem is, at any point in time, an eigenfunction of the Laplace s equation on a disk.] In mathematics, an eigenfunction of a linear operator, A , defined on some function space is any non zero function f in that space that… …   Wikipedia

• Mercer's theorem — In mathematics, specifically functional analysis, Mercer s theorem is a representation of a symmetric positive definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in (Mercer 1909), is one… …   Wikipedia

• Conjugate prior — Bayesian statistics Theory Bayesian probability Probability interpretations Bayes theorem Bayes rule · Bayes factor Bayesian inference Bayesian network Prior · Posterior · Likelihood …   Wikipedia