orcid.org/0000-0002-9771-3474
Search this author in Google Scholar

Articles: 2

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

Methods Funct. Anal. Topology 13 (2007), no. 2, 103-109

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 $A_{0}$, $A_{0}\subseteq A eq A_{0}$. 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 $\mathbb{L}_{2}(\mathbf{R}_{n})$.

### Damir Zyamovich Arov (to the 70th anniversary of his birth)

Methods Funct. Anal. Topology 10 (2004), no. 2, 1-3