New answers tagged fourier-analysis
3
votes
Eigenvalue of a convolution and a restriction?
Let me simultaneously (a) show why it is clear to me that user548030 is an AI, (b) work through some issues raised in its answer.
The first paragraph of user548030's answer restates (correctly) one ...
- 20.2k
1
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Sobolev inequalities and Wiener algebra
It is indeed false, (2) does not follow from (0) and $\nabla f\in L^2$. The idea is that since you consider the critical scaling, the potential inequality (on the Fourier side) fails both at $0$ and ...
- 6,476
3
votes
Accepted
Fourier transform of exponential over torus
This equality cannot be true in general. Indeed, let $m$ be any fixed nonzero real number, and let $r$ be a varying nonzero vector in $\Bbb R^2$ such that $|r|\to0$. Then the modulus of the left-hand ...
- 128k
0
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The Paley-Wiener theorem and exponential decay.
If you assume that $A=\hat{\omega}$ decays exponentially in both directions, i.e. $\exists\epsilon>0:\,\lim_{t\to \pm \infty} \hat{\omega}(t)e^{\epsilon t}=0$... or else you assume $\omega$ to be ...
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2
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Accepted
A question on finite Fourier series
No problem, this is doable already for $N=2$. The idea is as follows: at the point of the maximum first derivative must vanish, and yet we want to separate the maximum into two by adding something ...
- 6,476
1
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Approximate identities and pointwise convergence
There is an answer to this question in the book of Folland:
Folland, Gerald B. Real analysis: modern techniques and their applications. Vol. 40. John Wiley and Sons, 1999.
8.15 Theorem. Suppose $|\phi(...
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