| EPSRC Reference: |
GR/T25552/01 |
| Title: |
Convex Spectral Analysis |
| Principal Investigator: |
Safarov, Professor Y |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics |
| Organisation: |
Kings College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
10 June 2005 |
Ends: |
09 December 2008 |
Value (£): |
165,184
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
There has been an extensive study of various problems related to the numerical range of linear operators. However, even in the self-adjoint case, the consideration of the traditional one-dimensional numerical is not always sufficient (for instance, it does not give any information about the structure of the spectrum lying inside its convex hull). We propose to 'pull out' the usual numerical range into higher dimension and investigate the relation between this new multidimensional object and analytic properties of the corresponding operator (self-adjointness, dissipativity, relative compactness, and so on). The ultimate goal will be to find spectral characteristics of a general non-self-adjoint operator, which can be described in terms of its multidimensional numerical range. We also intend to consider several more specific problems related to the multidimensional numerical range. Possible applications include Szego type limit theorems for non-self-adjoint pseudodifferential operators with non-smooth symbols and new variational formulae for the spectrum of linear operators. It is anticipated that the multidimensional numerical range can be effectively studied by means of convex analysis, hence the title of the project.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
|