Inversion of Fredholm integral equations of the Mellin convolution type arising in atmospheric remote sensing.

Persistent Link:
http://hdl.handle.net/10150/187041
Title:
Inversion of Fredholm integral equations of the Mellin convolution type arising in atmospheric remote sensing.
Author:
Bevan, Edward James.
Issue Date:
1995
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
In this paper, the mathematics associated with simultaneous measurements of two parameters arising in the remote sensing of the atmosphere are cast in a form that permits the explicit solution for the eigenvalues and eigenfunctions. These eigenvalues and eigenfunctions are then used to deal with the ill-posed nature of the problem and ultimately to solve for the unknown atmospheric particle size density based on the information in both sets of measurements. The physical setting for this problem involves the measurement of optical transmission and the angular scattering of intensity. Using the Fraunhofer approximation and the van de Hulst anomalous diffraction approximation, the mathematics reduces to the inversion of Fredholm integral equations of the first kind in the special case known as a Mellin convolution. These equations are shown to be bounded and self-adjoint. Unfortunately, their inverse is seen to be unbounded and consequently the problem is ill-posed. The formulation of these equations to yield consistent, bounded, self-adjoint operators whose eigenfunctions and eigenvalues can be determined and addressing the ill-posed nature of the problem by exploiting the multisource data form the heart of this research.
Type:
text; Dissertation-Reproduction (electronic)
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Herman, Benjamin M.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleInversion of Fredholm integral equations of the Mellin convolution type arising in atmospheric remote sensing.en_US
dc.creatorBevan, Edward James.en_US
dc.contributor.authorBevan, Edward James.en_US
dc.date.issued1995en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIn this paper, the mathematics associated with simultaneous measurements of two parameters arising in the remote sensing of the atmosphere are cast in a form that permits the explicit solution for the eigenvalues and eigenfunctions. These eigenvalues and eigenfunctions are then used to deal with the ill-posed nature of the problem and ultimately to solve for the unknown atmospheric particle size density based on the information in both sets of measurements. The physical setting for this problem involves the measurement of optical transmission and the angular scattering of intensity. Using the Fraunhofer approximation and the van de Hulst anomalous diffraction approximation, the mathematics reduces to the inversion of Fredholm integral equations of the first kind in the special case known as a Mellin convolution. These equations are shown to be bounded and self-adjoint. Unfortunately, their inverse is seen to be unbounded and consequently the problem is ill-posed. The formulation of these equations to yield consistent, bounded, self-adjoint operators whose eigenfunctions and eigenvalues can be determined and addressing the ill-posed nature of the problem by exploiting the multisource data form the heart of this research.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairHerman, Benjamin M.en_US
dc.contributor.committeememberGreenlee, W.M.en_US
dc.contributor.committeememberLamb, George L.en_US
dc.identifier.proquest9528001en_US
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