Radon transform, spherical means, and an inverse problem for the wave equation

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Author(s)Yuan, Tao
Date Accessioned2018-03-13T11:43:43Z
Date Available2018-03-13T11:43:43Z
Publication Date2017
SWORD Update2017-11-10T17:18:50Z
AbstractConsider the linear map which sends the initial data to the trace, on the light cone with vertex at 0, of the solution of the initial value problem for the wave equation. We show this map is an isometry, construct its inverse, and give a partial characterization of its range. Our results are better in odd space dimensions than in the even dimensional case. Solutions of the wave equation can be expressed in terms of the spherical averages of the initial data and these spherical averages can be related to the Radon transform of a related function. We obtain our results exploiting this relationship and the isometry, the inversion formula and the range characterization of the Radon transform.en_US
AdvisorRakesh
DegreePh.D.
DepartmentUniversity of Delaware, Department of Mathematical Sciences
DOIhttps://doi.org/10.58088/zq19-0r43
Unique Identifier1028552059
URLhttp://udspace.udel.edu/handle/19716/23082
Languageen
PublisherUniversity of Delawareen_US
URIhttps://search.proquest.com/docview/2001286033?accountid=10457
KeywordsPure sciencesen_US
KeywordsInverse problemen_US
KeywordsInversionen_US
KeywordsIsometryen_US
KeywordsRadon transformen_US
KeywordsSpherical meanen_US
KeywordsWave equationen_US
TitleRadon transform, spherical means, and an inverse problem for the wave equationen_US
TypeThesisen_US
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Doctoral Dissertations (Winter 2014 to Present)