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Properties of the reconstruction algorithm and associated scattering transform for admittivities in the plane

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dc.contributor.authorVon Herrmann, Alan, author
dc.contributor.authorMueller, Jennifer, advisor
dc.date.accessioned2024-03-13T20:28:03Z
dc.date.available2024-03-13T20:28:03Z
dc.date.issued2009
dc.description.abstractWe consider the inverse admittivity problem in dimension two. The focus of this dissertation is to develop some properties of the scattering transform Sγ(k) with γ ϵ W1,p(Ω) and to develop properties of the exponentially growing solutions to the admittivity equation. We consider the case when the potential matrix is Hermitian and the definition of the potential matrix used by Francini [Inverse Problems, 16, 2000]. These exponentially growing solutions play a role in developing a reconstruction algorithm from the Dirichlet-to-Neumann map of γ. A boundary integral equation is derived relating the Dirichlet-to-Neumann map of γ to the exponentially growing solutions to the admittivity equation.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierETDF_Von_Herrmann_2009_3385183.pdf
dc.identifier.urihttps://hdl.handle.net/10217/238007
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.rights.licensePer the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users.
dc.subjectadmittivities
dc.subjectreconstruction algorithm
dc.subjectscattering transform
dc.subjectmathematics
dc.titleProperties of the reconstruction algorithm and associated scattering transform for admittivities in the plane
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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