arXiv subjects

Andreas Enblom

Publications and source records attributed to Andreas Enblom.

2 recordsLinked to original sources

arXiv2009

Lieb-Thirring Inequalities for Fourth-Order Operators in Low Dimensions

This paper considers Lieb-Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace inequality tr((-Delta)^2 - C^{HR}_{d,2} / (|x|^4) - V(x))^{-γ} < C_γ\int_{R^d} V(x)_+^{γ+ d/4} dx for gamma \geq 1 - d/4, where C^{HR}_{d,2} is the sharp constant in the Hardy-Rellich inequality and where C_γ> 0 is independent of V, is proved for dimensions d = 1,3. As a corollary of this inequality a Sobolev-type inequality is obtained.

math.SP↗

arXiv2008

Schroedinger Operators on Regular Metric Trees with Long Range Potentials: Weak Coupling Behavior

Consider a regular $d$-dimensional metric tree $Γ$ with root $o$. Define the Schroedinger operator $-Δ- V$, where $V$ is a non-negative, symmetric potential, on $Γ$, with Neumann boundary conditions at $o$. Provided that $V$ decays like $x^{-γ}$ at infinity, where $1 < γ\leq d \leq 2, γ\neq 2$, we will determine the weak coupling behavior of the bottom of the spectrum of $-Δ- V$. In other words, we will describe the asymptotical behavior of $\inf σ(-Δ- αV)$ as $α\to 0+$

math.SP↗