Spectral Theory Network  

Cardiff For several years the group at Cardiff (B. M. Brown, W. D. Evans, M. S. P. Eastham, K. M. Schmidt) has been working on analytic and computational problems associated with ODEs, PDEs and difference operators. Sometimes a numerical investigation has been undertaken to confirm an existing theoretical result , or to get some idea of its quantitative nature. On other occasions the results of numerical investigations have been used as pointers to the way that the analysis should proceed. This work programme has been undertaken both for selfadjoint and nonselfadjoint problems and has covered both differential and difference operators Methods have been developed which allow computer assisted proofs of theorems which have all the rigour of an analytic proof. Further work has been undertaken into the spectral theory of nonselfadjoint problems. Another area of activity in Cardiff is the spectral theory associated with operators of mathematical physics. A. Balinsky and W. D. Evans have worked on the stability of relativistic matter, semiclassical asymptotics, the existence, or otherwise, of zero modes of Pauli operators, and recently on spectral inequalities of Schrödinger operators with magnetic fields. Schmidt has studied the Dirac operator, in particular the appearance of dense point spectrum in suitably structured operators, spectral effects of the Klein paradox, and critical phenomena under singular perturbations. 

