Accumulation of resonances and eigenvalues for operators with distant perturbations

Abstract: We consider a model one-dimensional problem with distant perturbations, for which we study a phenomenon of emerging of infinitely many eigenvalues and resonances near the bottom of the essential spectrum. We show that they accumulate to a certain segment of the essential spectrum. Then we discuss possible generalization of this result to multi-dimensional models and various situations of resonances and eigenvalues distributions.

mathematical physicsanalysis of PDEsspectral theory

Audience: researchers in the topic

Quantum Circle