Imperial College London
Professor Ari Laptev

ProfessorAriLaptev

Faculty of Natural Sciences, Department of Mathematics

Chair in Pure Mathematics
 
 
 
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Contact

 

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

 
 
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Assistant

 

Mr David Whittaker +44 (0)20 7594 8481

 
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Location

 

680Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Laptev:2017:10.1063/1.4974360,
author = {Laptev, A and Sasane, SM},
doi = {10.1063/1.4974360},
journal = {Journal of Mathematical Physics},
title = {Perturbations of embedded eigenvalues for a magnetic Schrodinger operator on a cylinder},
url = {http://dx.doi.org/10.1063/1.4974360},
volume = {58},
year = {2017}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Perturbation problems for operators with embedded eigenvalues are generally challenging since the embedded eigenvalues cannot be separated from the rest of the spectrum. In this paper, we study a perturbation problem for embedded eigenvalues for a magnetic Schrödinger operator, when the underlying domain is a cylinder. The magnetic potential is C2 with an algebraic decay rate as the unbounded variable of the cylinder tends to ±∞. In particular, no analyticity of the magnetic potential is assumed. We also assume that the embedded eigenvalue of the unperturbed problem is not the square of an integer, thus avoiding the thresholds of the continuous spectrum of the unperturbed operator. We show that the set of nearby potentials, for which a simple embedded eigenvalue persists, forms a smooth manifold of finite codimension.
AU  - Laptev,A
AU  - Sasane,SM
DO  - 10.1063/1.4974360
PY  - 2017///
SN  - 0022-2488
TI  - Perturbations of embedded eigenvalues for a magnetic Schrodinger operator on a cylinder
T2  - Journal of Mathematical Physics
UR  - http://dx.doi.org/10.1063/1.4974360
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000395279200018&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/49267
VL  - 58
ER  -
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