| EPSRC Reference: |
GR/R81749/02 |
| Title: |
TOEPLITZ OPERATORS AND SPECTRAL THEORY OF NON-SELF-ADJOINT OPERATORS |
| Principal Investigator: |
Shargorodsky, Professor E |
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| Department: |
Mathematics |
| Organisation: |
Kings College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 March 2004 |
Ends: |
31 March 2006 |
Value (£): |
53,039
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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We intend to study (essential) spectra of Toeplitz operators with bounded measurable coefficients and eigenvalues of such operators embedded in the essential spectra. The aim is to minimize additional restrictions on coefficients. The motivation comes from applications to nonlinear problems of mechanics. It is well known that the properties of a Toeplitz operator with a coefficient A depend on the properties of the operator with the coefficient MAI . In linear problems of fluid dynamics and elasticity theory A depends on given data and MAI is usually piece-wise continuous. In nonlinear problems A may depend on the solution and have infinite number of zeros, in which case A/IAI may exhibit very complicated behaviour.We also intend to study basis problems for non-self-adjoint differential operators. In particular we plan to study the convergence rate of modified (for example Abel-type) summation schemes in terms of the eigenvectors depending upon the regularity of the function concerned, in the case when the the set of eigenvectors is complete but not a basis. The operators concerned arise in all fields of applied mathematics and physics, and we would expect to spend a proportion of the time studying non-self-adjoint problems which are drawn to our attention by colleagues and at conferences.
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Potential use in non-academic contexts |
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| Description |
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Sectors submitted by the Researcher |
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