Fredholm Integral Equation

An integral equation in which the integration domain is fixed and independent of the evaluation point, typically written either as ∫_{a}^{b} K(x,y)φ(y) dy = f(x) (first kind) or φ(x) − λ∫_{a}^{b} K(x,y)φ(y) dy = f(x) (second kind), often leading to compact operators on function spaces.