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MR2806693 (2012e:34020) 34A55 (34B24 34L40 47E05 49M30)
Chen, Xinfu; Cheng, Y. H.; Law, C. K. Reconstructing potentials from zeros of one eigenfunction. Trans. Amer. Math. Soc. 363 (2011), no. 9, 4831–4851.
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