| EPSRC Reference: |
GR/N19250/01 |
| Title: |
OPERATOR AND FUNCTION THEORY OF THE SYMMETRIZED BIDISC |
| Principal Investigator: |
Young, Professor N |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics and Statistics |
| Organisation: |
Newcastle University |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
22 May 2000 |
Ends: |
21 September 2000 |
Value (£): |
5,525
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
The VF will work intensively with the proposer on some function-theoretic problems with an engineering slant. Together we wish to resolve three questions:1. Do the Caratheodory and Kobayashi distances on the symmetrized bidisc ? coincide?2. What are necessary and sufficient conditions for analytic interpolation from the unit disc to ? ?3. How can suitable interpolating functions be constructed?The approach to these function-theoretic questions will be through the development of associated operator theory, with the aid of Agler's duality theory between families of tuples of commuting operators and cones of hereditary functions. We have identified promising lines for applying this theory to the construction of functions. We already have a necessary condition for question 2, and we know it to be sufficient in some special cases.We shall study possible counter-examples to sufficiency, and simultaneously pursue attempts to prove sufficiency, initially by trying to identify all totally geodesic discs in ?.The research forms part of a long term project, and in addition to the specific problems listed here, we shall investigate possible future generalization of our methods to other domains in Cn.
|
|
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: |
http://www.ncl.ac.uk |