| EPSRC Reference: |
GR/S14825/01 |
| Title: |
Fredholm Properties of Nonelliptic Operators |
| Principal Investigator: |
Shargorodsky, Professor E |
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| Department: |
Mathematics |
| Organisation: |
Kings College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
18 November 2003 |
Ends: |
17 February 2004 |
Value (£): |
7,944
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The modem geometric theory of hypoelliptic operators starts from L. Hormander's celebrated work on a class of second oreder operators, so called sums of squares of vector fields, and is one of the most beautiful and important parts of the theory of partial differential equations. It has intimate ties with multidimensional complex analysis, theory of Lie groups and stochastic analysis. L.P. Rothschild and E.M.Stein have demonstrated how one can learn a great deal about such operators on manifolds, by approximating by operators on homogeneous nilpotent Lie groups.It is well known that the so called Rockland condition is necessary (R. Beals) and sufficient (B. Helffer and J. Nourrigat) for the left invertibility (hypoellipticity) of a right-invariant homogeneous differential operator on a homogeneous Lie group. Right-invariant operators can be regarded as operators with constant coefficients . M. Christ, D. Geller, P. Glowacki and L. Polin have proved that the Rockland condition is sufficient for the existence of left parametrices for (and hence for hypoellipticity of) a wide class of pseudo-differential operators ( with variable coefficients ) on homogeneous Lie groups. Our aim is to show that the Rockland condition is also necessary for this.
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Potential use in non-academic contexts |
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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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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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