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On Sets that are Uniquely Determined by a Restricted Set of Integrals

1990
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Transactions of the American Mathematical Society
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In many applied areas, such as tomography and crystallography, one is confronted by an unknown subset 5 of a measure space (X, X) such as R" , or an unknown function 0 < (j> < 1 on X , having known moments (integrals) relative to a specified class F of functions f:X-*R. Usually, these F-moments do not fully determine the object S or function . We will say that 5 is a set of uniqueness if no other function 0 < y < 1 has the same F -moments as 5 in so far as the latter moments exist. Here, S is

doi:10.2307/2001708
fatcat:b5eiyk6hwncprdb6x433js44ne