期刊
JOURNAL OF FUNCTIONAL ANALYSIS
卷 248, 期 2, 页码 344-386出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2007.03.022
关键词
spherical mean operators; radon transforms; Darboux equation; tomography; range; inversion
类别
The transform considered in the paper averages a function supported in a ball in R-n over all spheres centered at the boundary of the ball. This Radon type transform arises in several contemporary applications, e.g. in thermoacoustic tomography and sonar and radar imaging. Range descriptions for such transforms are important in all these areas, for instance when dealing with incomplete data, error correction, and other issues. Four different types of complete range descriptions are provided, some of which also suggest inversion procedures. Necessity of three of these (appropriately formulated) conditions holds also in general domains, while the complete discussion of the case of general domains would require another publication. (c) 2007 Elsevier Inc. All rights reserved.
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