Wikipedia states that the function $f(x)=x^\alpha e^{-a|x|^2}$ for a multi-index $\alpha$ and a positive real number $a$ is in the Schwartz space. I need to find a function that is Schwartz but not a bump function. Could this be a fit? The function is smooth but its support are all real numbers expect $0$ which is not a compact set hence $f$ is not a bump function? Is this true?
2026-03-27 23:01:38.1774652498
Function that is in the Schwartz space but is not a bump function
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