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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| Language: | English |
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Universidad de La Frontera
2012-01-01
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| Series: | Cubo |
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000100004 |
| _version_ | 1818119496490024960 |
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| author | Mouez Dimassi Maher Zerzeri |
| author_facet | Mouez Dimassi Maher Zerzeri |
| author_sort | Mouez Dimassi |
| collection | DOAJ |
| 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" alt="Descripción: 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).<br>En este artículo estudiamos la expansión asintótica de la función shift espectral para perturbaciones de variación lenta de operadores periódicos de Schrödinger. Proporcionamos una expansión débil y puntual en potencias de h de la derivada de la función shift espectral que corresponde al par (P(h) = P0 + φ (hx); P0 = -Δ+ v(x)) ; donde<img border=0 width=189 height=35 id="_x0000_i1029" src="http://fbpe/img/cubo/v14n1/art04-01.jpg" alt="Descripción: http://fbpe/img/cubo/v14n1/art04-01.jpg"> es una función decreciente, O (|x|-δ) para algún δ > n y h un parámetro positivo pequeño. Aquí el potencial V es real, suave y periódico con respecto a un retículo T in Rn. Para demostrar la expansión asintótica puntual de la función shift espectral establecemos un teorema de absorción límite para P(h). |
| first_indexed | 2024-12-11T05:11:07Z |
| format | Article |
| id | doaj.art-9a2fb5f9be364630bce54565955d7918 |
| institution | Directory Open Access Journal |
| issn | 0716-7776 0719-0646 |
| language | English |
| last_indexed | 2024-12-11T05:11:07Z |
| publishDate | 2012-01-01 |
| publisher | Universidad de La Frontera |
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| spelling | doaj.art-9a2fb5f9be364630bce54565955d79182022-12-22T01:19:56ZengUniversidad de La FronteraCubo0716-77760719-06462012-01-011412947Spectral shift function for slowly varying perturbation of periodic Schrödinger operatorsMouez DimassiMaher ZerzeriIn 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" alt="Descripción: 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).<br>En este artículo estudiamos la expansión asintótica de la función shift espectral para perturbaciones de variación lenta de operadores periódicos de Schrödinger. Proporcionamos una expansión débil y puntual en potencias de h de la derivada de la función shift espectral que corresponde al par (P(h) = P0 + φ (hx); P0 = -Δ+ v(x)) ; donde<img border=0 width=189 height=35 id="_x0000_i1029" src="http://fbpe/img/cubo/v14n1/art04-01.jpg" alt="Descripción: http://fbpe/img/cubo/v14n1/art04-01.jpg"> es una función decreciente, O (|x|-δ) para algún δ > n y h un parámetro positivo pequeño. Aquí el potencial V es real, suave y periódico con respecto a un retículo T in Rn. Para demostrar la expansión asintótica puntual de la función shift espectral establecemos un teorema de absorción límite para P(h).http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000100004Periodic Schrödinger operatorspectral shift functionasymptotic expansionslimiting absorption theorem |
| spellingShingle | Mouez Dimassi Maher Zerzeri Spectral shift function for slowly varying perturbation of periodic Schrödinger operators Cubo Periodic Schrödinger operator spectral shift function asymptotic expansions limiting absorption theorem |
| title | 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_short | Spectral shift function for slowly varying perturbation of periodic Schrödinger operators |
| title_sort | spectral shift function for slowly varying perturbation of periodic schrodinger operators |
| topic | Periodic Schrödinger operator spectral shift function asymptotic expansions limiting absorption theorem |
| url | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000100004 |
| work_keys_str_mv | AT mouezdimassi spectralshiftfunctionforslowlyvaryingperturbationofperiodicschrodingeroperators AT maherzerzeri spectralshiftfunctionforslowlyvaryingperturbationofperiodicschrodingeroperators |