LOCALIZATION THEOREMS FOR NONLINEAR EIGENVALUE PROBLEMS

Let T : Omega -> C-nxn be a matrix-valued function that is analytic on some simply connected domain Omega subset of C A point lambda is an element of Omega is an eigenvalue if the matrix T(lambda) is singular. In this paper, we describe new localization results for nonlinear eigenvalue problems that generalize Gershgorin's theorem, pseudospectral inclusion theorems, and the Bauer-Fike theorem. We use our results to analyze three nonlinear eigenvalue problems: an example from delay differential equations, a problem due to Hadeler, and a quantum resonance computation.