integrable kernel
21Contact geometry — Contact form redirects here. For a web email form, see Form (web)#Form to email scripts. The standard contact structure on R3. Each point in R3 has a plane associated to it by the contact structure, in this case as the kernel of the one form dz − …
22Muckenhoupt weights — In mathematics, the class of Muckenhoupt weights Ap consists of those weights ω for which the Hardy–Littlewood maximal operator is bounded on Lp(dω). Specifically, we consider functions f on and their associated maximal functions M(f) defined as… …
23Atiyah–Singer index theorem — In the mathematics of manifolds and differential operators, the Atiyah–Singer index theorem states that for an elliptic differential operator on a compact manifold, the analytical index (closely related to the dimension of the space of solutions) …
24Integrability conditions for differential systems — In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage of… …
25Fredholm theory — In mathematics, Fredholm theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation. In a broader sense, the abstract structure of Fredholm s theory is… …
26Multiplier (Fourier analysis) — In Fourier analysis, a multiplier operator is a type of linear operator, or transformation of functions. These operators act on a function by altering its Fourier transform. Specifically they multiply the Fourier transform of a function by a… …
27Singular integral — In mathematics, singular integrals are central to abstract harmonic analysis and are intimately connected with the study of partial differential equations. Broadly speaking a singular intetgral is an integral operator: T(f)(x) = int K(x,y)f(y) ,… …
28Cauchy distribution — Not to be confused with Lorenz curve. Cauchy–Lorentz Probability density function The purple curve is the standard Cauchy distribution Cumulative distribution function …
29Malliavin calculus — The Malliavin calculus, named after Paul Malliavin, is a theory of variational stochastic calculus. In other words it provides the mechanics to compute derivatives of random variables. The original motivation for the development of the subject… …
30Eigenvalues 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… …
