Inverse scattering and distribution of resonances on the real line
(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 halfline, 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 superexponentially 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 halfline, 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 superexponentially 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 polefree strip and derive bounds on the location of the poles. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/39196
 author
 Hitrik, Michael ^{LU}
 supervisor
 opponent

 Professor Somersalo, Erkki, Instute of Mathematics, Helsinki University of Technology, Finland
 organization
 publishing date
 1998
 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
 19981210 10:15:00
 external identifiers

 other:ISRN: LUTFD2/TFMA98/1008SE
 ISBN
 9162832735
 language
 English
 LU publication?
 yes
 id
 08d816b539634668be99707e066dcaec (old id 39196)
 date added to LUP
 20160401 17:12:28
 date last changed
 20181121 20:47:30
@phdthesis{08d816b539634668be99707e066dcaec, 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 halfline, 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 superexponentially 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 polefree strip and derive bounds on the location of the poles.}}, author = {{Hitrik, Michael}}, isbn = {{9162832735}}, keywords = {{Mathematics; scattering poles; reflection coefficient; Schrödinger operator; inverse scattering; Matematik}}, language = {{eng}}, publisher = {{Department of Mathematics, Lund University}}, school = {{Lund University}}, title = {{Inverse scattering and distribution of resonances on the real line}}, year = {{1998}}, }