Examples of Functions in The Schwartz Space
- If i is a multi-index, and a is a positive real number, then
- Any smooth function f with compact support is in S(Rn). This is clear since any derivative of f is continuous and supported in the support of f, so (xαDβ) f has a maximum in Rn by the extreme value theorem.
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—Bernard Mandeville (1670–1733)
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