Zhislin's theorem revisited (Q1333795)

Zhislin's theorem gives a criterion for the atomic Schrödinger operator to have a finite number of bound states below its essential spectrum. Developing a general theory based on a function \(K\) introduced by S. Agmon (and which permits to study the operator in any given direction of the position space), the authors recover Zhislin's theorem as well as various other results concerning more general \((N+1)\)-body atomic-type operators. The theory is based on Sobolev-type and Hardy inequalities.