I am trying to solve the following equation, $f(x)-\mu\int_{0}^1\cos(2\pi(x-y))f(y)dy=g(x)$ but I am having some trouble. I know that if we look at this as an operator we get $(I-T)(f)=g(x)$ with $T(f)(x)=\int_{0}^{1}\cos(2\pi(x-y))f(y)dy$, we need to calculate the inverse of $I-T$ and this will be $\sum_{i=0}^{\infty}T^i$, with the condition that $||T||<1$, but I am not being able to find a good formula the values of $T^n$ so that I can get an "explicit" expression for $g$. Any help is aprecciated.
2026-03-26 16:08:55.1774541335
Solving a second order Fredholm's Integral equation
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