Schwartz distributions

pseudo-function δ such that an integral of δ(x-c)f(x) always takes the value of f(c)

discontinuous function whose value is zero for negative numbers and one for positive numbers

Green's functions

part of the domain of a mathematical function

integral transform and linear operator that takes a function of a real variable and produces another function of a real variable with a 90 degree phase shift

value that can be assigned to certain divergent integrals over a finite interval

a smooth and compactly supported function

function space of all functions whose derivatives are rapidly decreasing

space of holomorphic functions on the unit disk or upper half plane

solutions of a certain class of inhomogeneous partial differential equations

thumb|A mollifier (top) in Dimension (mathematics)|dimension one. At the bottom, in red is a function with a corner (left) and sharp jump (right), and in blue is its mollified version.

mathematical theorem on recovering a function from its Fourier transform

mathematical solution

Hilbert space equipped with a dense subspace that carries (in addition to the subspace topology) a finer topology such that the inclusion map is continuous

contnuous linear functional on the space of compactly supported differential forms