Imperial College London
Professor Ari Laptev

ProfessorAriLaptev

Faculty of Natural Sciences, Department of Mathematics

Chair in Pure Mathematics
 
 
 
//

Contact

 

+44 (0)20 7594 8499a.laptev Website

 
 
//

Assistant

 

Mr David Whittaker +44 (0)20 7594 8481

 
//

Location

 

680Huxley BuildingSouth Kensington Campus

//

Summary

 

Publications

Citation

BibTex format

@article{LAPTEV:2022:10.1007/s00205-022-01811-2,
author = {LAPTEV, AR and READ, LARRY and SCHIMMER, LUKAS},
doi = {10.1007/s00205-022-01811-2},
journal = {Archive for Rational Mechanics and Analysis},
title = {Calogero type bounds in two dimensions},
url = {http://dx.doi.org/10.1007/s00205-022-01811-2},
volume = {245},
year = {2022}
}
Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - For a Schrödinger operator on the plane R2 with electric potential V and an Aharonov–Bohm magnetic field, we obtain an upper bound on the number of its negative eigenvalues in terms of the L1(R2)-norm of V. Similar to Calogero’s bound in one dimension, the result is true under monotonicity assumptions on V. Our method of proof relies on a generalisation of Calogero’s bound to operator-valued potentials. We also establish a similar bound for the Schrödinger operator (without magnetic field) on the half-plane when a Dirichlet boundary condition is imposed and on the whole plane when restricted to antisymmetric functions.
AU  - LAPTEV,AR
AU  - READ,LARRY
AU  - SCHIMMER,LUKAS
DO  - 10.1007/s00205-022-01811-2
PY  - 2022///
SN  - 0003-9527
TI  - Calogero type bounds in two dimensions
T2  - Archive for Rational Mechanics and Analysis
UR  - http://dx.doi.org/10.1007/s00205-022-01811-2
UR  - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000829126500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://link.springer.com/article/10.1007/s00205-022-01811-2
UR  - http://hdl.handle.net/10044/1/99066
VL  - 245
ER  -
Download