Vol. 5, No. 5, 2012

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Schrödinger operators and the distribution of resonances in sectors

Tanya J. Christiansen

Vol. 5 (2012), No. 5, 961–982
Abstract

The purpose of this paper is to give some refined results about the distribution of resonances in potential scattering. We use techniques and results from one and several complex variables, including properties of functions of completely regular growth. This enables us to find asymptotics for the distribution of resonances in sectors for certain potentials and for certain families of potentials.

Keywords
Schrödinger operator, scattering theory, resonance
Mathematical Subject Classification 2010
Primary: 35P25, 81U05
Secondary: 47A40
Milestones
Received: 22 December 2010
Revised: 13 June 2011
Accepted: 24 October 2011
Published: 29 December 2012
Authors
Tanya J. Christiansen
Department of Mathematics
University of Missouri
Columbia, MO 65211
United States