| EPSRC Reference: |
GR/R40753/02 |
| Title: |
Block Operator Techniques for Systems of Differential Equations and Applications in Mathematical Physics |
| Principal Investigator: |
Tretter, Professor C |
| Other Investigators: |
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| Department: |
Mathematik |
| Organisation: |
University of Bremen |
| Scheme: |
Fast Stream |
| Starts: |
01 May 2002 |
Ends: |
31 October 2003 |
Value (£): |
41,183
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| EPSRC Research Topic Classifications: |
| Mathematical Analysis |
Mathematical Physics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Block operator matrices are matrices the entries of which are linear operators in Hilbert or Banach spaces. Operators of this form frequently arise in mathematical physics when studying systems of partial differential equations of mixed order and type, e.g., in quantum mechanics (Dirac operators, Klein Gordon operators), hydrodynamics (linearised Navier-Stokes operator), magnetohydrodynamics (ideal MHD equations), astrophysics, and impedance tomography. The aim of this project is to study the spectral properties of various classes of 2 x 2 block operator matrices in products of Hilbert spaces with unbounded entries. This includes localisation of the spectrum, qualitative structure of the spectrum (essential spectrum, embedded eigenvalues), accumulation, distribution and minimax principles of eigenvalues, completeness or basis properties of eigenfunctions and associated functions. Important tools for these investigations are, e.g., the recently introduced quadratic numerical range (a generalisation of the usual numerical range which gives a much better localisation of the spectrum), the spectral theory of operator functions, in particular, of the so-called Schur complements, and a transformation onto block diagonal form (allowing a reduction to two operators acting in one component of the given Hilbert space). The results obtained should be applied to a wide range of examples from the above mentioned areas.
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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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