Schwartz Space - Examples of Functions in The Schwartz Space

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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