The First Regularized Trace of the Sturm-Liouville Operator With Robin Boundary Conditions - Pavlović Komazec , Nataša; Vojvodić, Biljana (Sarajevo Journal of Mathematics, 2024)
This paper deals with the boundary value problem for the operator Sturm-Liouville type $ D^{2}=D^{2}(h, H, q_{1},q_{2},\tau,\varphi)$ generated by $$-y''(x)+\sum_{i=1}^{2}q_i(x)y(x-i\tau)=\lambda y(x),\,x\in[0, \pi]$$ $$y'(0)-hy(0)=0,\, y'(\pi)+Hy(\pi)=0$$ where $\ds{\frac{\pi}{3}\leq \tau <\frac{\pi}{2}}$,\,\,$ h, H\in R\setminus\{0\}$ and $\lambda $ is a spectral parameter. We assume that $ q_i$, $i=1,2$ are real-valued potential functions from $ L_2 [0, \pi]$. We establish a formula for the first regularized trace of this operator. 2020 Mathematics Subject Classification. 34B09, 34B24, 34L10