📂Banach Space

Fredholm Integral Equation

Definition¹

The integral equation given below is called the Fredholm Integral Equation of the first kind.

$$ g(s) = \int K(s, t) f(t) dt \tag{1} $$

Here, $K$ is referred to as the kernel. The following form is called the Fredholm Integral Equation of the second kind.

$$ g(s) = f(s) + \int K(s, t) f(t) dt \tag{2} $$

Explanation

Solving the integral equation $(1), (2)$ generally means finding $f$ that satisfies $(1), (2)$ for given $g$ and $K$.