CaltechAUTHORS
Published March 1995 | Version public
Journal Article Metadata-only

Absolute Summability of the Trace Relation for Certain Schrödinger Operators

Creators

  • 1. ROR icon University of Missouri
  • 2. ROR icon Norwegian University of Science and Technology
  • 3. ROR icon California Institute of Technology

Abstract

A recently established general trace formula for one-dimensional Schrödinger operators is systematically studied in the context of short-range potentials, potentials which approach different spatial asymptotes sufficiently fast, and appropriate impurity (defect) interactions in one-dimensional solids. We prove the absolute summability of the trace formula and establish its connections with scattering quantities, such as reflection coefficients, in each case.

Additional Information

© 1995 Springer-Verlag. Received: 4 February 1994. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material. We would like to thank Z. Zhao for numerous helpful discussions. F.G. is indebted to the Department of Mathematical Sciences of the University of Trondheim, Norway, and the Department of Mathematics at Caltech, Pasadena, CA for the hospitality extended to him in the summer of 1993. Support by the Norwegian Research Council (NFR) and by Caltech is gratefully acknowledged. H.H. is grateful to the Norwegian Research Council (NFR) for support. Communicated by T. Spencer.

Additional details

Identifiers

Eprint ID
85334
Resolver ID
CaltechAUTHORS:20180315-131739823

Funding

NSF
DMS-9101715
Norwegian Research Council

Dates

Created
2018-03-16
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Updated
2021-11-15
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Caltech Custom Metadata

Caltech groups
Mathematics Department , Physics Department