Some norm inequalities are presented for non- selfadjoint differential operators. First, the resolvent of the introduced non-selfadjoint differential operator using m-sectorial operators in the Hilbert space \(H=L_{2}(\Omega )\) is established. As application of this new result, the resolvent of the considered operator in the Hilbert space \(H^{\ell }=L_{2}(\Omega )^{\ell }\) is obtained utilizing some analytic techniques and diagonalizable way.

中文翻译：

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使用M扇形算子求解非自伴微分算子

对于非自伴微分算子，存在一些范式不等式。首先，建立了在希尔伯特空间\（H = L_ {2}（\ Omega）\）中使用m部门算子引入的非自伴微分算子的分解。作为该新结果的应用，利用一些解析技术和对角线化方法，获得了希尔伯特空间\（H ^ {\ ell} = L_ {2}（\ Omega）^ {\ ell} \）中考虑的算子的分解体。