V. M. Adamyan

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Articles: 2

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

Vadym Adamyan

↓ Abstract   |   Article (.pdf)

MFAT 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)

V. M. Adamyan, Yu. M. Berezansky, M. L. Gorbachuk, V. I. Gorbachuk, G. M. Gubreev, A. N. Kochubei, M. M. Malamud

MFAT 10 (2004), no. 2, 1-3


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