Pseudospectral theory
(by Brian Davies)
If one uses complex scaling to find resonances of a Schrodinger operator,
one has eventually to calculate the complex eigenvalues of a
non-self-adjoint Schrodinger operator. Experience over the last ten years
has shown that this is not merely a matter of extending standard theorems,
such as those dealing with the m-function, to the nsa context. Profound
issues of numerical stability arise, and have created an entirely new
subject called pseudospectral theory, which will be described.