| EPSRC Reference: |
GR/R91182/01 |
| Title: |
Matrix-valued harmonic functions and Fourier algebras on homogeneous spaces |
| Principal Investigator: |
Chu, Professor C |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Computing Department |
| Organisation: |
Goldsmiths College |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
08 May 2002 |
Ends: |
31 August 2002 |
Value (£): |
3,051
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Panel History: |
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Summary on Grant Application Form |
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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.
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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 |
| Summary |
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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.gold.ac.uk |