# Fredholm equation

A is an integral equation of the form

 $\int_{a}^{b}K(x,y)f(y)dy=g(x),\quad\forall x\in[a,b],$

and a Fredholm equation of the second kind is an integral equation of the form

 $f(x)-\lambda\int_{a}^{b}K(x,y)f(y)dy=g(x),\quad\forall x\in[a,b],$

where

 $Kf(x)=\int_{a}^{b}K(x,y)f(y)dy,\quad\forall x\in[a,b]$

is a compact operator in some function space.

Title Fredholm equation FredholmEquation 2013-03-22 15:49:59 2013-03-22 15:49:59 ncrom (8997) ncrom (8997) 5 ncrom (8997) Definition msc 45B05