# Tagged Questions

1answer
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### Decaying Fourier transform and smoothness

Suppose that $f\in L^1 (\mathbb{R})$ and that for any $n\in \mathbb{N}$ there is $C_n > 0$ such that its Fourier transform satisfies $$|\hat{f}(\xi )| \le C_n(1+|\xi |^2)^{-n}.$$ I want to show ...
1answer
118 views

### Convolution square root of $\delta$

I want to somehow classify the distributional solutions of the equation $$f \ast f = \delta$$ where $\delta = \delta _0$ is the Dirac delta distribution. Clearly, by Fourier transformation, we ...
0answers
65 views

### Different proofs of support theorem for Radon Transform

Let $\mathcal{H}$ be a set of all hyperplanes in $\mathbb{R}^n$. Radon transform of function $f(x) \colon \mathbb{R}^n \to \mathbb{R}$ is defined as function $R[f] \colon \mathcal{H} \to \mathbb{R}$ ...
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