A SPECTRAL EXPANSION FOR SCHRÖDINGER OPERATOR
In this paper we consider the SchrÄodinger operator L generated in L² (R+) by y" + q (x) y = μy; x ’ R+ := [0;∞) subject to the boundary condition y´ (0) - hy (0) = 0, where,q is a complex valued function summable in [0;∞ and h ≠ 0 is a complex c...
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| Autor principal: | |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2006
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172006000100005 |
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| Sumario: | In this paper we consider the SchrÄodinger operator L generated in L² (R+) by y" + q (x) y = μy; x ’ R+ := [0;∞) subject to the boundary condition y´ (0) - hy (0) = 0, where,q is a complex valued function summable in [0;∞ and h ≠ 0 is a complex constant, μ is a complex parameter. We have assumed that <img border=0 width=251 height=22 id="_x0000_i1026" src="http:/fbpe/img/proy/v25n1/2.jpg"> holds which is the minimal condition that the eigenvalues and the spectral singularities of the operator L are finite with finite multiplicities. Under this condition we have given the spectral expansion formula for the operator L using an integral representation for the Weyl function of L. Moreover we also have investigated the convergence of the spectral expansion |
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