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Schrodinger operators on regular metric trees with long range potentials: Weak coupling behavior

Ekholm, Tomas LU ; Enblom, Andreas and Kovarik, Hynek (2010) In Journal of Differential Equations 248(4). p.850-865
Abstract
Consider a regular d-dimensional metric tree Gamma with root o. Define the Schrodinger 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 <= d <= 2, gamma not equal 2, we will determine the weak coupling behavior of the bottom of the spectrum of -Delta -V. In other words. we will describe the asymptotic behavior of inf sigma(-Delta - alpha V) as alpha -> 0+. (C) 2009 Elsevier Inc. All rights reserved.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Fourier-Bessel transformation, Schrodinger operators, Metric trees, Weak coupling
in
Journal of Differential Equations
volume
248
issue
4
pages
850 - 865
publisher
Elsevier
external identifiers
  • wos:000274197200009
  • scopus:73549101079
ISSN
0022-0396
DOI
10.1016/j.jde.2009.11.011
language
English
LU publication?
yes
id
2e272008-9aa8-4017-ade4-ec64a4585d21 (old id 1570677)
date added to LUP
2010-03-17 08:19:24
date last changed
2018-05-29 09:51:00
@article{2e272008-9aa8-4017-ade4-ec64a4585d21,
  abstract     = {Consider a regular d-dimensional metric tree Gamma with root o. Define the Schrodinger 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 &lt;= gamma &lt;= d &lt;= 2, gamma not equal 2, we will determine the weak coupling behavior of the bottom of the spectrum of -Delta -V. In other words. we will describe the asymptotic behavior of inf sigma(-Delta - alpha V) as alpha -&gt; 0+. (C) 2009 Elsevier Inc. All rights reserved.},
  author       = {Ekholm, Tomas and Enblom, Andreas and Kovarik, Hynek},
  issn         = {0022-0396},
  keyword      = {Fourier-Bessel transformation,Schrodinger operators,Metric trees,Weak coupling},
  language     = {eng},
  number       = {4},
  pages        = {850--865},
  publisher    = {Elsevier},
  series       = {Journal of Differential Equations},
  title        = {Schrodinger operators on regular metric trees with long range potentials: Weak coupling behavior},
  url          = {http://dx.doi.org/10.1016/j.jde.2009.11.011},
  volume       = {248},
  year         = {2010},
}