A~discreteness criterion for the spectrum of a~quasielliptic operator

M. G. Gimadislamov

Matematičeskie zametki, Tome 9 (1971) no. 4, pp. 391-399.

Résumé

For the spectrum of the operator $$u=\sum_{j=1}^n{(-1)^{m_j}D_j^{2m_j}u+q(x)u},$$ to be discrete, where the mj are arbitrary positive integers such that $\sum_{j=1}^n{\frac1{2m_j}1}$, and $q(x)\ge 1$, it is necessary and sufficient that $\int\limits_K{q(x)dx\to\infty}$ , when the cube $K$ tends to infinity while preserving its dimensions.