Tagged Questions
2
votes
1answer
74 views
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 ...
4
votes
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 ...
1
vote
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 $R[f] \colon \mathcal{H} \to \mathbb{R}$ ...
