Representation Theorems for indefinite quadratic forms without spectral gap

Stephan Schmitz

Published 2014-09-08Version 1

The First and Second Representation Theorem for sign-indefinite quadratic forms are extended. We include new cases of unbounded forms associated with operators that do not necessarily have a spectral gap around zero. The kernel of the associated operators is determined for special cases. This extends results by Grubi\v{s}i\'c, Kostrykin, Makarov and Veseli\'c in [Mathematika 59 (2013), 169--189].