Let $H$ and $h$ be smooth functions of one and two variables respectively. Consider equation $$ H(x) = \int_\Bbb Rh(x,y)f(y)\mathrm dy \qquad \forall x\in \Bbb R. $$ When does it have a solution, and when this solution is unique? This is a Fredholm integral operator of the first kind, but I was not able to find a lot of literature on the existence and uniqueness. Also, what if we put an additional condition that $f$ is a probability density function, that is $f \geq 0$ and $\int_\Bbb Rf(y)\mathrm dy = 0$?
2025-01-13 05:47:04.1736747224
Integral equation: existence
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