Operator Methods in Diffraction

The following sections are included:

• Abstract operator theory

  • Hilbert space

  • Operators

  • Adjoint, symmetric and selfadjoint operators

  • Extension theory

• Space L₂ and differential operators

  • Hilbert space L₂

  • Generalized derivatives

  • Sobolev spaces and embedding theorems

• Problems of scattering

  • Harmonic operator

  • Bi-harmonic operator

  • Operator of fluid loaded plate

  • Another operator model of fluid loaded plate

• Extensions theory for differential operators

  • Zero-range potentials for harmonic operator

  • Zero-range potentials for bi-harmonic operator

  • Zero-range potentials for fluid loaded plates

  • Zero-range potentials for the plate with infinite crack