Summary: We consider an elliptic boundary value problem defined on a region \(\Omega\subset \mathbb{R}^n\) and involving an indefinite weight function \(\omega\). We also suppose that the problem under consideration admits a variational formulation. Then by appealing to the theory of selfadjoint operators acting in a Krein space, we derive various spectral properties for the problem. In particular, when \(\Omega\) is bounded we show that the principal vectors of our problem form a Riesz basis in \(L^2(\Omega^†;|\omega(x)|dx)\), where \(\Omega^†=\{x\in \Omega\mid \omega(x)\neq 0\}\), and also establish some results concerning their half-range completeness.
For the entire collection see [Zbl 0840.00035].