Tagged Questions

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Recovering function from convolution with a square function

Let $m : \mathbb{R} \to \mathbb{R}$ be a continuous function of compact support. Given $M$ as: $$M(x) = \int_{\mathbb{R}} m(t) (t+x)^2\ \mathrm{d}t,$$ is it possible recover $m$? I thought it ...
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How to deconvolve from the result of a sort of double convolution integral?

Say that I have a probability density function defined on the unit circle, $f_{\Theta}(\theta)$, with $\theta \in \left[0,2\pi\right)$. I have a joint pdf, assuming independence, of ...
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expanding convoluted integrand

I have a function on the form $$g(y) = \int_{-\infty}^{\infty}{e^{-v^2}f(y-v)dv}$$ I know that $g(y)$ is linear around $0$, $g(y\approx 0)\approx yG$, and I am interested in finding this gradient $G$. ...
Function with $|f(x)-\int^{\delta}_{-\delta}f(x+u)du|<\epsilon$
I am looking for a function $f:\mathbb{R}\to \mathbb{R}$ and $\epsilon>0$ such that there is no $\delta>0$, for him any $x\in\mathbb{R}$: $|f(x)-\int^{\delta}_{-\delta}f(x+u)du|<\epsilon$ ...