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{Ashbaugh:2016:10.1016/j.aim.2016.09.11,
author = {Ashbaugh, MS and Gesztesy, F and Laptev, A and Mitrea, M and Sukhtaiev, S},
doi = {10.1016/j.aim.2016.09.11},
journal = {Advances in Mathematics},
pages = {1108--1155},
title = {A bound for the eigenvalue counting function for Krein-von Neumann and Friedrichs extensions.},
url = {http://dx.doi.org/10.1016/j.aim.2016.09.11},
volume = {304},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - For an arbitrary open, nonempty, bounded set , , and sufficiently smooth coefficients , we consider the closed, strictly positive, higher-order differential operator in defined on , associated with the differential expression (equations missing) and its Krein–von Neumann extension in . Denoting by , , the eigenvalue counting function corresponding to the strictly positive eigenvalues of , we derive the bound (equations missing)where (with ) is connected to the eigenfunction expansion of the self-adjoint operator in defined on , corresponding to . Here denotes the (Euclidean) volume of the unit ball in (equations missing).Our method of proof relies on variational considerations exploiting the fundamental link between the Krein–von Neumann extension and an underlying abstract buckling problem, and on the distorted Fourier transform defined in terms of the eigenfunction transform ofin (equations missing)We also consider the analogous bound for the eigenvalue counting function for the Friedrichs extension in of (equations missing).
AU  - Ashbaugh,MS
AU  - Gesztesy,F
AU  - Laptev,A
AU  - Mitrea,M
AU  - Sukhtaiev,S
DO  - 10.1016/j.aim.2016.09.11
EP  - 1155
PY  - 2016///
SN  - 0001-8708
SP  - 1108
TI  - A bound for the eigenvalue counting function for Krein-von Neumann and Friedrichs extensions.
T2  - Advances in Mathematics
UR  - http://dx.doi.org/10.1016/j.aim.2016.09.11
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000398757500025&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/52741
VL  - 304
ER  -
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