Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior Academic Article uri icon

abstract

  • European Mathematical Society. Precise asymptotics known for the Green function of the Laplacian have found their analogs for bounded belowperiodic elliptic operators of the second-order belowand 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 coeficients in dimension d 2, when the gap edge occurs at a symmetry point of the Brillouin zone.

published proceedings

  • Journal of Spectral Theory

author list (cited authors)

  • Kha, M., Kuchment, P., & Raich, A.

citation count

  • 6

complete list of authors

  • Kha, Minh||Kuchment, Peter||Raich, Andrew

publication date

  • December 2017