Spectrum of quasielliptic differential operators (Q1326924)

This article deals with the spectrum in \(L_ 2\) of the selfadjoint differential operator \[ {\mathcal L} u = \sum_{(\alpha, \lambda) = 2} a_ \alpha D^ \alpha u + Q(x)u \] for which \[ \gamma_ 1 \sum_{\alpha \in P} | \xi^ \alpha |^ 2 \leq \sum_{(\alpha, \lambda) = 2} a_ \alpha (i \xi)^ \alpha \leq \gamma_ 2 \sum_{\alpha \in P} | \xi^ \alpha |^ 2 \] where \(\lambda = (p_ 1^{-1}, \dots, p_ n^{-1})\), \(P = \{(0, \dots, p_ i, \dots,0)\): \(i=1, \dots,n\}\) and \(Q(x)\) is measurable and locally bounded. Some statements on the structure of the negative part of \(sp({\mathcal L})\) are presented.