Rapidly decreasing Vanish at infinity

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refining concept, 1 can more closely rate of vanishing of functions @ infinity. 1 of basic intuitions of mathematical analysis fourier transform interchanges smoothness conditions rate conditions on vanishing @ infinity. rapidly decreasing test functions of tempered distribution theory smooth functions are



o(|x|)

for n, |x| → ∞, , such partial derivatives satisfy condition, too. condition set self-dual under fourier transform, corresponding distribution theory of tempered distributions have same property.







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