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: BASCANBAZ-TUNCA,GULEN
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2006
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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 = &#956;y; x &#8217; R+ := [0;&#8734;) subject to the boundary condition y´ (0) - hy (0) = 0, where,q is a complex valued function summable in [0;&#8734; and h &#8800; 0 is a complex constant, &#956; 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