| EPSRC Reference: |
GR/J74640/01 |
| Title: |
TWO - TERM SPECTRAL ASYMPTOTICS FOR PARTIAL DIFFERENTIAL OPERATORS |
| Principal Investigator: |
Vassiliev, Professor D |
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| Department: |
Sch of Mathematical & Physical Sciences |
| Organisation: |
University of Sussex |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 1994 |
Ends: |
31 January 1998 |
Value (£): |
114,418
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Summary on Grant Application Form |
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Consider the eigenvalue problem for a linear positive self adjoint elliptic differential operator of order 2m acting on a compact n-dimensional manifold with boundary. Denote by N ( ) the counting function (number of eigenvalues below a given ). In 1983 H Weyl conjectured that it might be possible to derive a two-term asymptotic formula for N ( ) as For m=1 the Weyl conjecture was proved by V Ivrii and R Melrose in 1980, and for arbitrary m- by D Vassiliev in 1983. The aim of the research programme is to develop these results and the associated mathematical technique by:(1) Studying geometric conditions under which the Weyl conjecture is true;(2) Creating a calculus of global oscillatory integrals with complex phase;(3) Producing new Fourier Tauberian theorems;(4) Proving an analogue of the Weyl conjecture for domains with fractal boundary (this is the so called Berry conjecture);(5) Obtaining similar asymptotic formulae describing the distribution of eigenvalues in the problem of trapped modes;(6) Conducting numerical experiments, especially in the fractal case.
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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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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Further Information: |
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| Organisation Website: |
http://www.sussex.ac.uk |