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

M. G. Gimadislamov

Bashkir State University

Abstract: 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.

UDC: 517.9

Received: 14.01.1975

 English version: Mathematical Notes, 1976, 20:5, 957–961

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