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

Journal of the European Mathematical Society (2008)

- Volume: 010, Issue: 3, page 739-755
- ISSN: 1435-9855

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topEkholm, 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 -

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