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an inverse problem related to gaussian integral

Suppose we have a function $\rho(x,t)$ defined over $[-1,1]\times[0,1]$. Define the integral $ f_T(x)=\int_{[0,1]} (\rho(.,t)*K_{T-t})(x) dt $ for $x\in R$ and $T>1$, where $*$ is the convolution, an …
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