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:2019:10.1063/1.5093401,
author = {Laptev, A and Schimmer, L and Takhtajan, LA},
doi = {10.1063/1.5093401},
journal = {Journal of Mathematical Physics},
pages = {1--10},
title = {Weyl asymptotics for perturbed functional difference operators},
url = {http://dx.doi.org/10.1063/1.5093401},
volume = {60},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We consider the difference operator HW = U + U−1 + W, where U is the self-adjoint Weyl operator U = e−bP, b > 0, and the potential W is of the form W(x) = x2N + r(x) with N∈ and |r(x)| ≤ C(1 + |x|2N−) for some 0 <  ≤ 2N − 1. This class of potentials W includes polynomials of even degree with leading coefficient 1, which have recently been considered in Grassi and Mariño [SIGMA Symmetry Integrability Geom. Methods Appl. 15, 025 (2019)]. In this paper, we show that such operators have discrete spectrum and obtain Weyl-type asymptotics for the Riesz means and for the number of eigenvalues. This is an extension of the result previously obtained in Laptev et al. [Geom. Funct. Anal. 26, 288–305 (2016)] for W = V + ζV−1, where V = e2πbx, ζ > 0.
AU  - Laptev,A
AU  - Schimmer,L
AU  - Takhtajan,LA
DO  - 10.1063/1.5093401
EP  - 10
PY  - 2019///
SN  - 0022-2488
SP  - 1
TI  - Weyl asymptotics for perturbed functional difference operators
T2  - Journal of Mathematical Physics
UR  - http://dx.doi.org/10.1063/1.5093401
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000506019500040&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://aip.scitation.org/doi/10.1063/1.5093401
UR  - http://hdl.handle.net/10044/1/76568
VL  - 60
ER  -
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