Conditions for the self-adjointness of a~quasi-elliptic operator

M. G. Gimadislamov

Matematičeskie zametki, Tome 20 (1976) no. 5, pp. 709-716.

Résumé

We prove the following theorem for the operator $L=\sum_{k=1}^n(-1)^{m_k}D_k^{2m_k}+q$ considered in $L_2(R^n)$ (the $m_k$ are natural numbers): If $q(x)\ge-C\max\limits_k|x_k|^{\frac1{1-1/2m_k}}$ ($C>0$) for sufficiently large $|x|$, then L is a self-adjoint operator.