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Results tagged with fourier-analysis
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user 381188
The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.
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How to prove the Fourier transform of $e^{-x^p}$ is positive [duplicate]
I wonder how to prove that
$$\int_0^\infty\exp(-x^p)\cos(tx)\,dt\geq 0, \quad \frac{1}{2}<p<1.$$
This conclusion is used in the answer to another question here
Looking for sufficient conditions for po …
- 61
4
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1
answer
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Fourier-positivity of a certain function
I am wondering how to prove the below Fourier transform is non-negative? I did much simulation and it seems to be non-negative.
$$\int_0^\inf (be^{-at^p}-ae^{-bt^p})\cos(tx)dt, 0<a<b, \frac{1}{2}<p<1$ …
- 61