First Regularized Trace of the Limit Assignment of Sturm-Liouville Type With Two Constant Delays

Nataša Pavlović, Milenko Pikula, Biljana Vojvodić

We observe spectral assignment $D^2y=\lambda y$ defined by \begin{align} -&y''(x)+q_1(x)y(x-au_1)+q_2(x)y(x-au_2)=ambda y(x), ambda=z^2 &q_1(x),q_2(x)ı L_1[0,i], au_1,au_2ı(0,i)otag &y(x-au_1)\equiv0, xı(0,au_1], au_1=k_0au_2 &y(i)=0 \end{align} In this paper, we construct a solution $y(x,z)$ which satisfies (1) and (2), and then (3) is used to construct the characteristic function $F(z)$, $z\in C$. Then the asymptotics of eigenvalues of the operator $D^2$ is constructed. Finally, the first regularized trace is calculated.