Conditions for the self-adjointness of a quasi-elliptic operator期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	M G Gimadislamov

Institution:	(1) Bashkir State University, USSR

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 m_k 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.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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