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Distributional derivative of the Heaviside step function
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Dirac delta function
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For every test function
φ
,
⟨
H
′
,
φ
⟩
=
−
∫
0
∞
φ
′
(
t
)
d
t
=
φ
(
0
)
,
(446)
so
H
′
=
δ
as distributions.
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Dirac delta function
Distribution theory
Analysis
Area of mathematics
Mathematics
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