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

abstract

• AbstractPrecise 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 bandgap 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.

authors

• Kuchment, Peter

published proceedings

• MATHEMATISCHE NACHRICHTEN

author list (cited authors)

• Kuchment, P., & Raich, A.

citation count

• 21

complete list of authors

• Kuchment, Peter||Raich, Andrew

publication date

• October 2012

publisher

• Wiley  Publisher

published in

• Mathematische Nachrichten  Journal

keywords

• 35j15
• 35p05
• 47a10
• 47f05
• 47n20
• Asymptotics
• Elliptic Operator
• Green's Function
• Msc (2010) 35j08
• Periodic Operator
• Resolvent Estimate
• Spectral Edge

Digital Object Identifier (DOI)

• 10.1002/mana.201100272

start page

• 1880

end page

• 1894

volume

• 285

issue

• 14-15

URL

• https://doi.org/10.1002/mana.201100272