An overview of periodic elliptic operators Academic Article uri icon

abstract

  • © 2016 American Mathematical Society. The article surveys the main topics, techniques, and results of the theory of periodic operators arising in mathematical physics and other areas. Close attention is paid to studying analytic properties of Bloch and Fermi varieties, which significantly influence most spectral features of such operators. The approaches described are applicable not only to the standard model example of Schrödinger operator with periodic electric potential -Δ+V (x), but to a wide variety of elliptic periodic equations and systems, equations on graphs, ∂-operator, and other operators on abelian coverings of compact bases. Important applications are mentioned. However, due to the size restrictions, they are not dealt with in detail.

altmetric score

  • 1

author list (cited authors)

  • Kuchment, P.

citation count

  • 50

publication date

  • April 2016