Hi,

I was wondering if there were known solutions to the following homogeneous Fredholm integral equation:

$\displaystyle f(x) = \int_0^1 \frac{2xy}{x+y} f(y) dy$

And more generally to:

$\displaystyle f(x) = \int_0^1 \sqrt{xy}\phi(\log(\frac{y}{x})) f(y) dy$

where $\displaystyle \phi(x)$ is a symmetric function.

Thanks by advance for your help.

Alexis