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
Materias:	Spectrum Weyl Function Spectral Expansion
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172006000100005
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spelling	oai:scielo:S0716-091720060001000052006-06-07A SPECTRAL EXPANSION FOR SCHRÖDINGER OPERATORBASCANBAZ-TUNCA,GULEN Spectrum Weyl Function Spectral Expansion 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 expansioninfo:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.25 n.1 20062006-05-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172006000100005en10.4067/S0716-09172006000100005
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Spectrum Weyl Function Spectral Expansion
spellingShingle	Spectrum Weyl Function Spectral Expansion BASCANBAZ-TUNCA,GULEN A SPECTRAL EXPANSION FOR SCHRÖDINGER OPERATOR
description	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
author	BASCANBAZ-TUNCA,GULEN
author_facet	BASCANBAZ-TUNCA,GULEN
author_sort	BASCANBAZ-TUNCA,GULEN
title	A SPECTRAL EXPANSION FOR SCHRÖDINGER OPERATOR
title_short	A SPECTRAL EXPANSION FOR SCHRÖDINGER OPERATOR
title_full	A SPECTRAL EXPANSION FOR SCHRÖDINGER OPERATOR
title_fullStr	A SPECTRAL EXPANSION FOR SCHRÖDINGER OPERATOR
title_full_unstemmed	A SPECTRAL EXPANSION FOR SCHRÖDINGER OPERATOR
title_sort	spectral expansion for schrödinger operator
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2006
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172006000100005
work_keys_str_mv	AT bascanbaztuncagulen aspectralexpansionforschrodingeroperator AT bascanbaztuncagulen spectralexpansionforschrodingeroperator
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A SPECTRAL EXPANSION FOR SCHRÖDINGER OPERATOR

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