Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior
Minh Kha, Peter Kuchment, Andrew Raich · Journal of Spectral Theory · 2017
Precise asymptotics known for the Green function of the Laplacian have found their analogs for bounded below periodic elliptic operators of the second-order below and at the bottom of the spectrum. Due to the band-gap structure of the spectra of such operators, the question arises whether similar results can be obtained near or at the edges of spectral gaps. In a previous work, two of the authors considered the case of a spectral edge. The main result of this article is finding such asymptotics near a gap edge, for “generic” periodic elliptic operators of second-order with real coefficients in dimension d ≥ 2 , when the gap edge occurs at a symmetry point of the Brillouin zone.