# Fredholm equation

A Fredholm equation of the first kind is an integral equation^{} of the form

$${\int}_{a}^{b}K(x,y)f(y)\mathit{d}y=g(x),\forall x\in [a,b],$$ |

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

$$f(x)-\lambda {\int}_{a}^{b}K(x,y)f(y)\mathit{d}y=g(x),\forall x\in [a,b],$$ |

where

$$Kf(x)={\int}_{a}^{b}K(x,y)f(y)\mathit{d}y,\forall x\in [a,b]$$ |

is a compact operator^{} in some function space^{}.

Title | Fredholm equation |
---|---|

Canonical name | FredholmEquation |

Date of creation | 2013-03-22 15:49:59 |

Last modified on | 2013-03-22 15:49:59 |

Owner | ncrom (8997) |

Last modified by | ncrom (8997) |

Numerical id | 5 |

Author | ncrom (8997) |

Entry type | Definition |

Classification | msc 45B05 |