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

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

2008-09-10

arxiv.org/abs/0809.1845v1

Jour. of Diff. Eq. 248 (2010) 850-865

Mathematics

Spectral Theory

Scientific paper

10.1016/j.jde.2009.11.011

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

Affiliated with

Also associated with

No associations

Rating

Schroedinger Operators on Regular Metric Trees with Long Range Potentials: Weak Coupling Behavior does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Schroedinger Operators on Regular Metric Trees with Long Range Potentials: Weak Coupling Behavior, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Schroedinger Operators on Regular Metric Trees with Long Range Potentials: Weak Coupling Behavior will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-161919