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arXiv math-ph/0701004math-phmath.MP
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非负自伴算子的非负扰动

Non-negative perturbations of non-negative self-adjoint operators

Vadym Adamyan

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08 pages
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摘要：

设$A$是Hilbert空间$\mathcal{H}$中的非负自伴算子，$A_{0}$是$A_{0}$的某个稠密闭约束，$A_{0}\subseteq A \neq A_{0}$ .了解$A$是否是$\mathcal{H}$中$A_{0}$的唯一非负自伴扩张是一个有趣的问题。我们给出了一个自然的标准，这是这种情况下，如果它失败，我们描述了所有的非负扩展的$A_{0}$。所得到的结果被应用于研究$\mathbb{L}_{2}(\mathbf{R}_{n})$中Laplace算子和多调和算子的非负奇点扰动。

英文摘要：

Let $A$ be a non-negative self-adjoint operator in a Hilbert space $\mathcal{H}$ and $A_{0}$ be some densely defined closed restriction of $A_{0}$, $A_{0}\subseteq A \neq A_{0}$. It is of interest to know whether $A$ is the unique non-negative self-adjoint extensions of $A_{0}$ in $\mathcal{H}$. We give a natural criterion that this is the case and if it fails, we describe all non-negative extensions of $A_{0}$. The obtained results are applied to investigation of non-negative singular point perturbations of the Laplace and poly-harmonic operators in $\mathbb{L}_{2}(\mathbf{R}_{n})$.

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