Abstract We show global uniqueness in the fractional Calderon problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work [10] considered the case of infinitely many measurements. The method is again based on the strong uniqueness properties for the fractional equation, this time combined with a unique continuation principle from sets of measure zero. We also give a constructive procedure for determining an unknown potential from a single exterior measurement, based on constructive versions of the unique continuation result that involve different regularization schemes.

中文翻译：

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具有单一测量的分数 Calderón 问题的唯一性和重构

摘要 我们使用单一测量和外部任意、可能不相交的子集的数据显示分数卡尔德隆问题的全局唯一性。之前的工作 [10] 考虑了无限多次测量的情况。该方法再次基于分数方程的强唯一性属性，这次结合了来自测度零集的独特延续原则。我们还基于涉及不同正则化方案的独特延续结果的建设性版本，给出了从单个外部测量中确定未知势的建设性程序。