Displaying similar documents to “Zeros of the Jost function for a class of exponentially decaying potentials.”

Resonances for Schrödinger operators with compactly supported potentials

T. J. Christiansen, P. D. Hislop (2008)

Journées Équations aux dérivées partielles

Similarity:

We describe the generic behavior of the resonance counting function for a Schrödinger operator with a bounded, compactly-supported real or complex valued potential in d 1 dimensions. This note contains a sketch of the proof of our main results [, ] that generically the order of growth of the resonance counting function is the maximal value d in the odd dimensional case, and that it is the maximal value d on each nonphysical sheet of the logarithmic Riemann surface in the even dimensional...

Spectral properties of non-self-adjoint operators

Johannes Sjöstrand (2009)

Journées Équations aux dérivées partielles

Similarity:

This text contains a slightly expanded version of my 6 hour mini-course at the PDE-meeting in Évian-les-Bains in June 2009. The first part gives some old and recent results on non-self-adjoint differential operators. The second part is devoted to recent results about Weyl distribution of eigenvalues of elliptic operators with small random perturbations. Part III, in collaboration with B. Helffer, gives explicit estimates in the Gearhardt-Prüss theorem for semi-groups.