Inhaltszusammenfassung

This thesis is devoted to the Representation Theorems for symmetric indefinite (that is non-semibounded) sesquilinear forms and their applications. In particular, we consider the case where the operator associated with the form does not have a spectral gap around zero. Furthermore, the relation between reducing graph subspaces, solutions to operator Riccati equations, and block diagonalisation of diagonally dominant block operator matrices is investigated. By means of the Representation...This thesis is devoted to the Representation Theorems for symmetric indefinite (that is non-semibounded) sesquilinear forms and their applications. In particular, we consider the case where the operator associated with the form does not have a spectral gap around zero. Furthermore, the relation between reducing graph subspaces, solutions to operator Riccati equations, and block diagonalisation of diagonally dominant block operator matrices is investigated. By means of the Representation Theorems, a corresponding relation is established for operators associated with indefinite forms and form Riccati equations. In this framework, an explicit block diagonalisation and a spectral decomposition of the Stokes operator as well as a representation for its kernel are obtained. We apply the Representation Theorems to forms given by hgrad u, h(·) grad vi, where the coefficient matrices h(·) are allowed to be sign-indefinite. As a result, indefinite self-adjoint differential operators div h(·) grad with homogeneous Dirichlet or Neumann boundary conditions are constructed. Examples of such kind are operators related to the modelling of optical metamaterials and left-indefinite Sturm-Liouville operators. » weiterlesen» einklappen

Autoren

Klassifikation

DFG Fachgebiet:
Mathematik

DDC Sachgruppe:
Mathematik