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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

BASCANBAZ-TUNCA, GULEN. A SPECTRAL EXPANSION FOR SCHRÖDINGER OPERATOR. Proyecciones (Antofagasta) [online]. 2006, vol.25, n.1, pp.63-78. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172006000100005.

In this paper we consider the SchrÄodinger operator L generated in L2 (R+) by y" + q (x) y = μy; xR+ := [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 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

Keywords : Spectrum; Weyl Function; Spectral Expansion.

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