Category
page 1Schwartz distributions
Dirac delta function
pseudo-function δ such that an integral of δ(x-c)f(x) always takes the value of f(c)
Heaviside step function
discontinuous function whose value is zero for negative numbers and one for positive numbers
Green's function
Green's functions
support
part of the domain of a mathematical function
Hilbert transform
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
Cauchy principal value
value that can be assigned to certain divergent integrals over a finite interval
bump function
a smooth and compactly supported function
Schwartz space
function space of all functions whose derivatives are rapidly decreasing
Hardy space
space of holomorphic functions on the unit disk or upper half plane
fundamental solution
solutions of a certain class of inhomogeneous partial differential equations
Mollifier
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.
Fourier inversion theorem
mathematical theorem on recovering a function from its Fourier transform
weak solution
mathematical solution
rigged Hilbert space
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
current
contnuous linear functional on the space of compactly supported differential forms