Spectral shift function for slowly varying perturbation of periodic Schrödinger operators

In this paper we study the asymptotic expansion of the spectral shift function for the slowly varying perturbations of periodic Schrödinger operators. We give a weak and pointwise asymptotic expansions in powers of h of the derivative of the spectral shift function corresponding to the pair(P(h) = P...

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Autores principales:	Dimassi,Mouez, Zerzeri,Maher
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2012
Materias:	Periodic Schrödinger operator spectral shift function asymptotic expansions limiting absorption theorem
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000100004
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spelling	oai:scielo:S0719-064620120001000042018-10-08Spectral shift function for slowly varying perturbation of periodic Schrödinger operatorsDimassi,MouezZerzeri,Maher Periodic Schrödinger operator spectral shift function asymptotic expansions limiting absorption theorem In this paper we study the asymptotic expansion of the spectral shift function for the slowly varying perturbations of periodic Schrödinger operators. We give a weak and pointwise asymptotic expansions in powers of h of the derivative of the spectral shift function corresponding to the pair(P(h) = P0 + φ (hx); P0 = -Δ+ v(x)) ; where<img border=0 width=189 height=35 id="_x0000_i1030" src="http:/fbpe/img/cubo/v14n1/art04-01.jpg"> is a decreasing function, O (\|x\|-δ) for some δ> n and h is a small positive parameter. Here the potential V is real, smooth and periodic with respect to a lattice T in Rn. To prove the pointwise asymptotic expansion of the spectral shift function, we establish a limiting absorption Theorem for P(h).info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.14 n.1 20122012-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000100004en10.4067/S0719-06462012000100004
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Periodic Schrödinger operator spectral shift function asymptotic expansions limiting absorption theorem
spellingShingle	Periodic Schrödinger operator spectral shift function asymptotic expansions limiting absorption theorem Dimassi,Mouez Zerzeri,Maher Spectral shift function for slowly varying perturbation of periodic Schrödinger operators
description	In this paper we study the asymptotic expansion of the spectral shift function for the slowly varying perturbations of periodic Schrödinger operators. We give a weak and pointwise asymptotic expansions in powers of h of the derivative of the spectral shift function corresponding to the pair(P(h) = P0 + φ (hx); P0 = -Δ+ v(x)) ; where<img border=0 width=189 height=35 id="_x0000_i1030" src="http:/fbpe/img/cubo/v14n1/art04-01.jpg"> is a decreasing function, O (\|x\|-δ) for some δ> n and h is a small positive parameter. Here the potential V is real, smooth and periodic with respect to a lattice T in Rn. To prove the pointwise asymptotic expansion of the spectral shift function, we establish a limiting absorption Theorem for P(h).
author	Dimassi,Mouez Zerzeri,Maher
author_facet	Dimassi,Mouez Zerzeri,Maher
author_sort	Dimassi,Mouez
title	Spectral shift function for slowly varying perturbation of periodic Schrödinger operators
title_short	Spectral shift function for slowly varying perturbation of periodic Schrödinger operators
title_full	Spectral shift function for slowly varying perturbation of periodic Schrödinger operators
title_fullStr	Spectral shift function for slowly varying perturbation of periodic Schrödinger operators
title_full_unstemmed	Spectral shift function for slowly varying perturbation of periodic Schrödinger operators
title_sort	spectral shift function for slowly varying perturbation of periodic schrödinger operators
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2012
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000100004
work_keys_str_mv	AT dimassimouez spectralshiftfunctionforslowlyvaryingperturbationofperiodicschrodingeroperators AT zerzerimaher spectralshiftfunctionforslowlyvaryingperturbationofperiodicschrodingeroperators
_version_	1714206775915315200

Spectral shift function for slowly varying perturbation of periodic Schrödinger operators

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