Schrodinger operators on regular metric trees with long range potentials: Weak coupling behavior
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1570677
- author
- Ekholm, Tomas LU ; Enblom, Andreas and Kovarik, Hynek
- organization
- publishing date
- 2010
- 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
- 2016-04-01 10:28:19
- date last changed
- 2022-01-25 23:37:23
@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 <= 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.}}, author = {{Ekholm, Tomas and Enblom, Andreas and Kovarik, Hynek}}, issn = {{0022-0396}}, keywords = {{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}}, doi = {{10.1016/j.jde.2009.11.011}}, volume = {{248}}, year = {{2010}}, }