A spectral expansion for Schrödinger operator

  • Gülen Bascanbaz-Tunca Ankara University.
Palabras clave: Spectrum, Weyl function, spectral expansion, espectro, función de Weyl, expansión espectral.

Resumen

In this paper we consider the Schrödinger operator L generated inL²(R₊) byy''+q(x)y= µy, x∈R₊:= [0, ∞)subject to the boundary conditiony'(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 thatholds 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.

Biografía del autor/a

Gülen Bascanbaz-Tunca, Ankara University.
Faculty of Science,Department of Mathematics.

Citas

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Publicado
2017-05-08
Cómo citar
[1]
G. Bascanbaz-Tunca, A spectral expansion for Schrödinger operator, PJM, vol. 25, n.º 1, pp. 63-78, may 2017.
Sección
Artículos