Examples of positive operators in Krein space with 0 a regular critical point of infinite rank

Abstract

It is shown that the operators associated with the perturbed wave equation in ℝn and with elliptic operators with an indefinite weight function and mildly varying coefficients on ℝn are similar to a self-adjoint operator in a Hilbert space. These operators have the whole ℝn as the spectrum. It is shown that they are positive operators in corresponding Krein spaces, and the whole problem is reduced to showing that 0 is not a singular critical point.