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Scaling property of the Fourier transform
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If
f
λ
(
x
)
=
f
(
λ
x
)
on
R
n
with
λ
>
0
, then
f
λ
(
ξ
)
=
λ
−
n
f
(
ξ
/
λ
)
,
(257)
and consequently
∥
f
λ
∥
p
=
λ
−
n
/
p
∥
f
∥
p
,
∥
f
λ
∥
q
=
λ
−
n
(
1
−
1/
q
)
∥
f
∥
q
.
(258)
Table of contents
56
1
Scaling necessity for an Lp to Lq Fourier bound
Scaling property of the Fourier transform
34
Ancestors
(5)
Fourier transform
Analysis
Area of mathematics
Mathematics
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