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MR1942115 (2004g:58021) 58J05 (35J10 47F05)
Braverman, M.; Milatovich, O.; Shubin, M. Essential selfadjointness of Schrödinger-type operators on manifolds. (Russian) Uspekhi Mat. Nauk 57 (2002), no. 4(346), 3--58; translation in Russian Math. Surveys 57 (2002), no. 4, 641–692
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