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

DOI10.4171/JST/188zbMath1394.35297arXiv1508.06703MaRDI QIDQ680710

Minh Kha, Andrew S. Raich, Peter A. Kuchment

Publication date: 26 January 2018

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.06703

zbMATH Keywords

Green's functionperiodic coefficientsspectral gapsFloquet transformsecond order elliptic operatorBrillouin zone

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectrum, resolvent (47A10) Second-order elliptic equations (35J15) Schrödinger operator, Schrödinger equation (35J10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Green's functions for elliptic equations (35J08)

Related Items (7)

Green's function asymptotics of periodic elliptic operators on abelian coverings of compact manifolds ⋮ Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown ⋮ High-energy homogenization of a multidimensional nonstationary Schrödinger equation ⋮ Degenerate band edges in periodic quantum graphs ⋮ Generic properties of dispersion relations for discrete periodic operators ⋮ Virtual bound levels in a gap of the essential spectrum of the weakly perturbed periodic Schrödinger operator ⋮ An overview of periodic elliptic operators

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