$\nabla $ | Gradient operator |

${\nabla}^{2}$ | Laplacian operator |

$i$ | Sqrt(−1) |

${k}_{o}$ | Wave-number |

$\widehat{E}$ | Symbol of the operator |

$\oplus $ | Direct sum |

$D=\frac{\partial}{\partial k}$ | Derivatives in Sobolev space |

${H}^{2}$ | Sobolev space with 2 derivatives |

${R}_{\lambda}\left(k\right)$ | Resolvent |

$P$ | Projector |

${G}_{\lambda}\left(x-y\right)$ | Green's function |