 Scaling property of the Fourier transform

ID: scaling-property-of-the-fourier-transform

Codex  0 Created 2026-09-24 Updated 2026-09-28

f_{λ} (x) = f (λ x)

R^{n}

with

λ > 0

, then

f_{λ} (ξ) = λ^{- n} f (ξ / λ),

and consequently

∥ f_{λ} ∥_{p} = λ^{- n / p} ∥ f ∥_{p}, ∥ f_{λ} ∥_{q} = λ^{- n (1 - 1/ q)} ∥ f ∥_{q} .

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