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Existence and Uniqueness of Volterra integral equations of the first kind

$$ \int_0^t k(s,t)f(s)ds=g(t) $$ To prove the existence and uniqueness of solutions of Volterra integral equation(VIE) of the first kind, we usually differentiate it and convert to the VIE of the ...
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A question on Radon transform

In the book of Helgason which is called "Radon transform and integral geometry", he defines on page 2 the Radon transform on hyperplanes as: $$ \hat{f}(\xi) = \int_{\xi} f(x) dm(x)$$ Where $dm(x)$ ...