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MR2068979 35B27 (34E15 35B10 35P05)
Birman, M. Sh. On the averaging procedure for periodic operators in a neighborhood of an edge of an internal gap. (Russian) Algebra i Analiz 15 (2003), no. 4, 61--71; translation in St. Petersburg Math. J. 15 (2004), no. 4, 507–513
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