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: | , |
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| Lenguaje: | English |
| Publicado: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2012
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000100004 |
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| Sumario: | 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). |
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