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Inverse scattering and distribution of resonances on the real line

Hitrik, Michael LU (1998)
Abstract
We study aspects of scattering theory for the Schrödinger operator on the real line. In the first part of the thesis we consider potentials supported by a half-line, and we are interested in the inverse problem of reconstruction of the potential from the knowledge of values of the reflection coefficient at equidistributed points on the positive imaginary axis. Under the assumption of exponential decay of the potential, Hölder type stability estimates for this problem are obtained. In the second part of the thesis we study the distribution of scattering poles for the class of super-exponentially decaying potentials. Sharp upper bounds on the counting function of the poles in discs are derived and the density of resonances in strips is... (More)
We study aspects of scattering theory for the Schrödinger operator on the real line. In the first part of the thesis we consider potentials supported by a half-line, and we are interested in the inverse problem of reconstruction of the potential from the knowledge of values of the reflection coefficient at equidistributed points on the positive imaginary axis. Under the assumption of exponential decay of the potential, Hölder type stability estimates for this problem are obtained. In the second part of the thesis we study the distribution of scattering poles for the class of super-exponentially decaying potentials. Sharp upper bounds on the counting function of the poles in discs are derived and the density of resonances in strips is estimated. We also obtain estimates on the width of a pole-free strip and derive bounds on the location of the poles. (Less)
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author
opponent
  • Professor Somersalo, Erkki, Instute of Mathematics, Helsinki University of Technology, Finland
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Mathematics, scattering poles, reflection coefficient, Schrödinger operator, inverse scattering, Matematik
pages
77 pages
publisher
Department of Mathematics, Lund University
defense location
Department of Mathematics, 1in Room C
defense date
1998-12-10 10:15
external identifiers
  • other:ISRN: LUTFD2/TFMA-98/1008-SE
ISSN
0347-8475
ISBN
91-628-3273-5
language
English
LU publication?
yes
id
08d816b5-3963-4668-be99-707e066dcaec (old id 39196)
date added to LUP
2007-06-21 13:19:49
date last changed
2016-09-19 08:44:59
@phdthesis{08d816b5-3963-4668-be99-707e066dcaec,
  abstract     = {We study aspects of scattering theory for the Schrödinger operator on the real line. In the first part of the thesis we consider potentials supported by a half-line, and we are interested in the inverse problem of reconstruction of the potential from the knowledge of values of the reflection coefficient at equidistributed points on the positive imaginary axis. Under the assumption of exponential decay of the potential, Hölder type stability estimates for this problem are obtained. In the second part of the thesis we study the distribution of scattering poles for the class of super-exponentially decaying potentials. Sharp upper bounds on the counting function of the poles in discs are derived and the density of resonances in strips is estimated. We also obtain estimates on the width of a pole-free strip and derive bounds on the location of the poles.},
  author       = {Hitrik, Michael},
  isbn         = {91-628-3273-5},
  issn         = {0347-8475},
  keyword      = {Mathematics,scattering poles,reflection coefficient,Schrödinger operator,inverse scattering,Matematik},
  language     = {eng},
  pages        = {77},
  publisher    = {Department of Mathematics, Lund University},
  school       = {Lund University},
  title        = {Inverse scattering and distribution of resonances on the real line},
  year         = {1998},
}