Measures on double or resonant eigenvalues for linear Schrödinger operator

In this paper we consider linear Schrödinger operator with double or resonant eigenvalues. The main result is the bound of the measure (in a suitable space of functions) of the potentials leading to such double or resonant eigenvalues. Namely we present measure type estimates evaluating neighborhoods of the socalled double or resonant set. © 2007 Elsevier Inc. All rights reserved.