TY - JOUR

T1 - Approximate commutativity for a decaying potential and a function of an elliptic operator

AU - Sloushch, V.A.

PY - 2015

Y1 - 2015

N2 - For a continuous function $ \varphi (\lambda )$, $ \lambda \in \mathbb{R}$, with compact support, a bounded function $ W(x)$, $ x\in \mathbb{R}^{d}$, with power-like asymptotics at infinity, and a suitable selfadjoint operator $ H$ in $ L_{2}({\mathbb{R}}^{d})$, estimates for the singular values of the operator $ \varphi (H)W-W\varphi (H)$ are considered. It is proved that the singular values of $ \varphi (H)W-W\varphi (H)$ decay faster than those of $ \varphi (H)W$. A relationship between the singular values asymptotics for the operators $ \varphi (H)W$ and $ \varphi ^{n}(H)W^{n}$ is also established. - See more at: http://www.ams.org/journals/spmj/2015-26-05/S1061-0022-2015-01362-9/#sthash.QmnAJspJ.dpuf

AB - For a continuous function $ \varphi (\lambda )$, $ \lambda \in \mathbb{R}$, with compact support, a bounded function $ W(x)$, $ x\in \mathbb{R}^{d}$, with power-like asymptotics at infinity, and a suitable selfadjoint operator $ H$ in $ L_{2}({\mathbb{R}}^{d})$, estimates for the singular values of the operator $ \varphi (H)W-W\varphi (H)$ are considered. It is proved that the singular values of $ \varphi (H)W-W\varphi (H)$ decay faster than those of $ \varphi (H)W$. A relationship between the singular values asymptotics for the operators $ \varphi (H)W$ and $ \varphi ^{n}(H)W^{n}$ is also established. - See more at: http://www.ams.org/journals/spmj/2015-26-05/S1061-0022-2015-01362-9/#sthash.QmnAJspJ.dpuf

KW - Elliptic differential operators

KW - integral operators

KW - estimates for singular values

KW - classes of compact operators - See more at: http://www.ams.org/journals/spmj/2015-26-05/S1061-0022-2015-01362-9/#sthash.QmnAJspJ.dpuf

U2 - 10.1090/spmj/1362

DO - 10.1090/spmj/1362

M3 - Article

VL - 26

SP - 849

EP - 857

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 5

ER -