Abstract
We prove the following theorem for the operator\(L = \sum\nolimits_{k = 1}^n {( - 1)^m k} D_k^{2m} k + q\) considered in L2(Rn) (the mk are natural numbers): If\(q(x) \ge - C\mathop {\max }\limits_k \left| {x_k } \right|^{^{\frac{1}{{1 - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}m_k }}} } (C > 0)\) for sufficiently large |x|, then L is a self-adjoint operator.
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Translated from Matematicheskie Zametki, Vol. 20, No. 5, pp. 709–716, November, 1976.
In conclusion I wish to thank R. S. Ismagilov for useful advice.
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Gimadislamov, M.G. Conditions for the self-adjointness of a quasi-elliptic operator. Mathematical Notes of the Academy of Sciences of the USSR 20, 957–961 (1976). https://doi.org/10.1007/BF01146918
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DOI: https://doi.org/10.1007/BF01146918