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Statements
⟨
ℱ
(
1
)
,
ϕ
⟩
=
2
π
⟨
ℱ
(
ℱ
(
δ
)
)
,
ϕ
⟩
=
2
π
⟨
ℱ
(
δ
)
,
ℱ
(
ϕ
)
⟩
=
2
π
⟨
δ
,
ℱ
(
ℱ
(
ϕ
)
)
⟩
=
2
π
⟨
δ
,
ϕ
-
⟩
=
2
π
ϕ
(
0
)
,
distribution
distributional-Fourier-transform
1
italic-ϕ
2
distribution
distributional-Fourier-transform
distributional-Fourier-transform
delta-distribution
italic-ϕ
2
distribution
distributional-Fourier-transform
delta-distribution
ℱ
italic-ϕ
2
distribution
delta-distribution
ℱ
ℱ
italic-ϕ
2
distribution
delta-distribution
subscript
italic-ϕ
2
italic-ϕ
0
{\displaystyle{\displaystyle\left\langle\mathscr{F}\left(1\right),\phi\right%
\rangle=\sqrt{2\pi}\left\langle\mathscr{F}\left(\mathscr{F}\left(\delta\right)%
\right),\phi\right\rangle=\sqrt{2\pi}\left\langle\mathscr{F}\left(\delta\right%
),\mathscr{F}(\phi)\right\rangle=\sqrt{2\pi}\left\langle\delta,\mathscr{F}(%
\mathscr{F}(\phi))\right\rangle=\sqrt{2\pi}\left\langle\delta,\phi_{-}\right%
\rangle=\sqrt{2\pi}\phi(0),}}
π
{\displaystyle{\displaystyle\pi}}
δ
x
Dirac-delta-distribution
𝑥
{\displaystyle{\displaystyle\delta_{x}}}
⟨
Λ
,
ϕ
⟩
distribution
Λ
italic-ϕ
{\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right%
\rangle}}
ℱ
(
u
)
distributional-Fourier-transform
𝑢
{\displaystyle{\displaystyle\mathscr{F}\left(\NVar{u}\right)}}
ℱ
(
ϕ
)
ℱ
italic-ϕ
{\displaystyle{\displaystyle\mathscr{F}(\phi)}}
ϕ
(
x
)
italic-ϕ
𝑥
{\displaystyle{\displaystyle\phi(x)}}
Identifiers
