Dirac delta function (in distributional sense)
GPTKB entity
Statements (49)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
generalized function
|
| gptkbp:alsoKnownAs |
delta distribution
|
| gptkbp:application |
gptkb:probability_theory
gptkb:sampling_theory acoustics control theory electromagnetism engineering mathematical physics mechanics modeling point sources probability density of a discrete random variable |
| gptkbp:approximation |
sequence of functions converging to δ in distributional sense
|
| gptkbp:category |
tempered distributions
Schwartz distributions |
| gptkbp:codomain |
real numbers
|
| gptkbp:compatibleWith |
function in the classical sense
|
| gptkbp:defines |
δ(φ) = φ(0) for all test functions φ
|
| gptkbp:distributionalDerivative |
distributional derivative of δ is δ'
|
| gptkbp:domain |
space of test functions
|
| gptkbp:FourierTransform |
1
|
| gptkbp:generalizes |
higher-dimensional delta distributions
|
| https://www.w3.org/2000/01/rdf-schema#label |
Dirac delta function (in distributional sense)
|
| gptkbp:integralOverRealLine |
1
|
| gptkbp:introduced |
gptkb:Paul_Dirac
|
| gptkbp:LaplaceTransform |
1
|
| gptkbp:property |
gptkb:organization
translation invariant scaling property generalized eigenfunction of the differentiation operator convolution identity for distributions even distribution homogeneous distribution of degree -1 linear functional sifting property singular support at 0 unit impulse |
| gptkbp:relatedTo |
gptkb:Heaviside_step_function
impulse response fundamental solution |
| gptkbp:supports |
{0}
|
| gptkbp:symbol |
δ(x)
|
| gptkbp:usedIn |
gptkb:signal_processing
gptkb:Green's_functions Fourier analysis partial differential equations quantum mechanics |
| gptkbp:bfsParent |
gptkb:Fejér_kernel
|
| gptkbp:bfsLayer |
7
|