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Zbl 0880.34018
El-Reheem, Z.F.A.
On some trace formula for the Sturm-Liouville operator.
(English)
[J] PU.M.A., Pure Math. Appl. 7, No.1-2, 61-68 (1996). ISSN 1218-4586

The Sturm-Liouville equation $-y''+q(x)y=\mu \rho(x)y$ is considered on $[0,\infty)$ with $y(0)=0$. The weight coefficient $\rho$ is discontinuous: $\rho(x)=-1$ for $0\le x\le 1$, and $\rho(x)=1$ for $x>1$. The potential function $q:[0,\infty)\to [0,\infty)$ satisfies $\int_0^\infty (1+x)q(x) dx<\infty$. The parameter $\mu$ takes complex values. A trace formula is given for this Sturm-Liouville operator.
[Tibor Krisztin (Szeged)]
MSC 2000:
*34B05 Linear boundary value problems of ODE
34L05 General spectral theory for ODE
34L25 Scattering theory (ODE)

Keywords: Sturm-Liouville operator; boundary value problem; trace formula

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