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Results tagged with fa.functional-analysis
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user 57410
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
1
answer
578
views
Decay rate of the convolution of two functions
Let $f(x)=e^{-\frac{x^2}{2}}$ ($x\in\mathbb{R}$), and $g\in C^{\infty}(\mathbb{R})$ with $|g(x)|=O(e^{-k|x|^{\gamma}})$ as $|x|\to\infty$, for $k>0$, $\gamma>0$. Let $h=f*g$, the convolution of $f$ an …
- 24.2k
5
votes
1
answer
1k
views
A example on Fourier tranform of a continous compactly supported function
I am trying to find a continuous compactly supported function $f$ such that the Fourier transform $f^{ft}$ and derivative $(f^{ft})'$ of the $f^{ft}$ decay faster than exponential rates, that is
$$|f^ …
- 8,086