Validated computation for infinite dimensional eigenvalue problems

In this paper we will show how guaranteed bounds for eigenvalues (together with eigenvectors) are obtained and how non-existence of eigenvalues in a concrete region could be assured. Some examples for several types of operators in bounded and unbounded domains will be presented. We will furthermore discuss possible future applications to eigen- value enclosing/excluing of Schr ¨odinger operator, hopefully in its spectral gaps.