Range conditions for a spherical mean transform
Range conditions for a spherical mean transform
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球均值变换的范围条件
DOI：
10.3934/ipi.2009.3.373
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
P. Kuchment
中科院分区：
文献类型：
--
作者：
M. Agranovsky;David V. Finch;P. Kuchment
本文致力于范围描述的Radon型变换，平均一个功能在所有领域的中心，一个给定的领域。这种变换自然出现在热声层析成像，一种新的医学成像方法。最近已经获得了这样的变换的范围描述，并包括光滑性和支持条件，矩条件，和一些额外的谱性质的正交性条件。已经注意到，在奇数维中，令人惊讶的是，力矩条件是多余的，可以消除。这段经文表明，事实上在任何维度都发生同样的事情。
The paper is devoted to the range description of the Radon type transform that averages a function over all spheres centered on a given sphere. Such transforms arise naturally in thermoacoustic tomography, a novel method of medical imaging. Range descriptions have recently been obtained for such transforms, and consisted of smoothness and support conditions, moment conditions, and some additional orthogonality conditions of spectral nature. It has been noticed that in odd dimensions, surprisingly, the moment conditions are superfluous and can be eliminated. It is shown in this text that in fact the same happens in any dimension.