Functional Analysis and Applications Seminar 

07/10/2005, 15:00 — 16:00 — Room P3.10, Mathematics Building
Vladimir Rabinovich, Instituto Politecnico Nacional, Mexico

Essential spectrum of the main operators of quantum mechanics.

The aim of the talk is to present a new approach to the investigation of the essential spectra of the main operators of quantum mechanics. We include these operators in a class of pseudodifferential operators perturbed by non-smooth potentials. For an operator under consideration we introduce a family of limit operators, and prove that the essential spectrum of the original operator is the union of spectra of limit operators. Since the limit operators have more simple structure than the original operator, we obtain a strong tool for the investigation of the essential spectra of differential and pseudodifferential operators. We apply this method to the study of the essential spectra of the Schrödinger, Klein-Gordon, and Dirac operators and to a new simple proof of the classical Hunziker-van Winter-Zjislin Theorem.