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Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case
Author(s) -
Kuchment Peter,
Raich Andrew
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100272
Subject(s) - mathematics , elliptic operator , spectral line , operator (biology) , spectrum (functional analysis) , laplace operator , mathematical analysis , dimension (graph theory) , enhanced data rates for gsm evolution , function (biology) , order (exchange) , spectral theory , laplace transform , pure mathematics , physics , quantum mechanics , chemistry , telecommunications , biochemistry , finance , repressor , hilbert space , evolutionary biology , biology , computer science , transcription factor , economics , gene
Precise asymptotics known for the Green's function of the Laplace operator have found their analogs for periodic elliptic operators of the second order at and below 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. As the result of this work shows, this is possible at a spectral edge when the dimension d ≥ 3.