Lieb–Thirring inequalities on the half-line with critical exponent

Ekholm, Tomas, and Frank, Rupert. "Lieb–Thirring inequalities on the half-line with critical exponent." Journal of the European Mathematical Society 010.3 (2008): 739-755. <http://eudml.org/doc/277386>.

@article{Ekholm2008,
abstract = {We consider the operator $-d^2/dr^2-V$ in $L_2(\mathbb \{R\}_+)$ with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound $\mathrm \{tr\}(-d^2/dr^2-V)_-^\gamma \le C_\{\gamma ,\alpha \}\int _\{\mathbb \{R\}_+\}(V(r)-1/(4r^2))_+^\{\gamma +(1+\alpha )/2\}r^\alpha dr$ for any $\alpha \in [0,1)$ and $\gamma \ge (1-\alpha )/2$. This includes a Lieb-Thirring inequality in the critical endpoint case.},
author = {Ekholm, Tomas, Frank, Rupert},
journal = {Journal of the European Mathematical Society},
keywords = {Schrödinger operator; Lieb–Thirring inequalities; Hardy inequality; Schrödinder operator; Lieb-Thirring inequalities; Hardy inequality},
language = {eng},
number = {3},
pages = {739-755},
publisher = {European Mathematical Society Publishing House},
title = {Lieb–Thirring inequalities on the half-line with critical exponent},
url = {http://eudml.org/doc/277386},
volume = {010},
year = {2008},
}

TY - JOUR
AU - Ekholm, Tomas
AU - Frank, Rupert
TI - Lieb–Thirring inequalities on the half-line with critical exponent
JO - Journal of the European Mathematical Society
PY - 2008
PB - European Mathematical Society Publishing House
VL - 010
IS - 3
SP - 739
EP - 755
AB - We consider the operator $-d^2/dr^2-V$ in $L_2(\mathbb {R}_+)$ with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound $\mathrm {tr}(-d^2/dr^2-V)_-^\gamma \le C_{\gamma ,\alpha }\int _{\mathbb {R}_+}(V(r)-1/(4r^2))_+^{\gamma +(1+\alpha )/2}r^\alpha dr$ for any $\alpha \in [0,1)$ and $\gamma \ge (1-\alpha )/2$. This includes a Lieb-Thirring inequality in the critical endpoint case.
LA - eng
KW - Schrödinger operator; Lieb–Thirring inequalities; Hardy inequality; Schrödinder operator; Lieb-Thirring inequalities; Hardy inequality
UR - http://eudml.org/doc/277386
ER -