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Precise asymptotics known for the Green's function of the Laplace operatorhave found their analogs for periodic elliptic operators of the second order atand below the bottom of the spectrum. Due to the band-gap structure of thespectra of such operators, the question arises whether similar results can beobtained near or at the edges of spectral gaps. As the result of this workshows, this is possible at a spectral edge in dimensions d>2.

Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case