| EPSRC Reference: |
GR/R91182/02 |
| Title: |
Matrix-valued harmonic functions and Fourier algebras on homogeneous spaces |
| Principal Investigator: |
Chu, Professor C |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Sch of Mathematical Sciences |
| Organisation: |
Queen Mary University of London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 September 2002 |
Ends: |
31 July 2003 |
Value (£): |
1,687
|
| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
In an EPSRC-funded project (98/99), the Invesitgator and the nominated VF found an interesting connection between harmonic analyis and Jordan algebras which opened a new and exciting direction of research, impacting both of these areas. These results will be published in a research monograph by Springer-Verlag. The Investigator and the VF plan to pursue further research in this direction, and to extend their results to matrix-valued harmonic functions and homogeneous spaces. The first task is to study the algebraic analytic structures of the space of bounded matrix-valued harmonic functions on homogeneous spaces, in particular, to construct a Jordan triple product for these functions and to seek a Poisson space to represent them.There is a non-commutative analogue to the space of bounded complex-valued harmonic functions, namely, the space of harmonic functionals on the Fourier algebra of a homogeneous space. The second task is to study the structrues of these harmonic functionals and the Banach algebra properties of their predual, and to construct a Jordan triple product for these functionals. The novelty is the exploitation of the link between harmonic analysis and non-associative functional analysis. The propsoed research should give some new insights into the structures of harmonic functions.
|
|
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: |
|