Can someone give an example of Schwartz space function that doesn't decay exponentially?
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What do you mean by exponential decay? – Davide Giraudo Oct 28 '13 at 21:42
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1I mean that it is not exponentially small at infinity. That is I need a function f in Schwartz space st for all a>0, e^(a|x|^a)f doesn't belong to L^infty. – SOM Oct 28 '13 at 22:02
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Consider your favorite bump function construction and replace the exponential function by $$e(x)=\sum_{k=0}^\infty \frac{x^k}{\sqrt{k!}}$$
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