Properties
- S(Rn) is a Fréchet space over the complex numbers.
- From Leibniz' rule, it follows that S(Rn) is also closed under pointwise multiplication: if f, g ∈ S(Rn), then fg ∈ S(Rn).
- If 1 ≤ p ≤ ∞, then S(Rn) ⊂ Lp(Rn).
- The space of all bump functions, C∞
c(Rn), is included in S(Rn).
- The Fourier transform is a linear isomorphism S(Rn) → S(Rn).
- If f ∈ S(R), then f is uniformly continuous on R.
Read more about this topic: Schwartz Space
Famous quotes containing the word properties:
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—John Locke (1632–1704)
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