Topic summary
Rapidly decreasing
Extracted from the Wikipedia article Vanish at infinity.
Rapidly decreasing
Refining the concept, one can look more closely to the rate of vanishing of functions at infinity. One of the basic intuitions of mathematical analysis is that the Fourier transform interchanges smoothness conditions with rate conditions on vanishing at infinity. Using big O notation, the rapidly decreasing test functions of tempered distribution theory are smooth functions that are