| EPSRC Reference: |
GR/R53210/01 |
| Title: |
The Spectral Shift Function and The Integrated Density Of States |
| Principal Investigator: |
Pushnitski, Dr A |
| Other Investigators: |
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| Department: |
School of Mathematics |
| Organisation: |
Loughborough University |
| Scheme: |
Fast Stream |
| Starts: |
07 February 2002 |
Ends: |
06 October 2003 |
Value (£): |
63,953
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The spectral shift function and the integrated density of states are two fundamental objects of spectral theory of partial differential operators. Both of them come from some regularization of the trace of the spectral projection. For the spectral shift function, the regularization is achieved, roughly speaking, by subtracting the trace of the spectral projection of a non-perturbed operator from the trace of the spectral projection of a perturbed one. For the integrated density of states it is achieved by dividing the trace of the projection of an operator, restricted to a large finite domain, by the volume of this domain.As the applicant has observed recently, the spectral shift function and the integrated density of states of the Schrodinger operator are related by a simple and explicit asymptotic formula, which provides a new insight into the spectral theory of partial differential operators. This formula has been justified so far only for a very restrictive class of operators.The aim of the project is to study the revealed link between the spectral shift function and the integrated density of states for a wide class of Schrodinger operators and other operators of mathematical physics.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.lboro.ac.uk |