A spectral expansion for Schrödinger operator


  • Gülen Bascanbaz-Tunca Ankara University.




Spectrum, Weyl function, spectral expansion, espectro, función de Weyl, expansión espectral.


In this paper we consider the Schrödinger operator L generated in
L²(R+) by
y''+q(x)y= µy; x ∈ R+ := [0, ∞)
subject to the boundary condition
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.

Author Biography

Gülen Bascanbaz-Tunca, Ankara University.

Faculty of Science,
Department of Mathematics.


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How to Cite

G. Bascanbaz-Tunca, “A spectral expansion for Schrödinger operator”, Proyecciones (Antofagasta, On line), vol. 25, no. 1, pp. 63-78, May 2017.