

Kings College,
London
E B Davies has worked
on the spectral analysis of selfadjoint Schrödinger operators for
over twenty years, and is the author of two monographs in this general
area. In the
last four years he has turned his interests to the nonselfadjoint theory,
which is far less well understood. He has obtained some of the first bounds
on the locations of complex eigenvalues. These are important for reducing
the work involved in trying to locate them numerically. He has proved
that the larger eigenvalues of many nonselfadjoint differential operators
are highly unstable. As a result any algorithm used to compute
them is bound to run into difficulties. He has also become one of the
experts in the subject of pseudospectral theory, which raises a lot of
new perspectives in the field and leads to new questions. Several of these
papers have a strong computational side. The nonselfadjoint theory has
very close connections with the theory of resonances via the theory of
complex scaling and exterior complex scaling, and he has obtained new
results in this area in collaboration with A Aslanyan and A Abramov.
