The First Regularized Trace of the Sturm-Liouville Operator With Robin Boundary Conditions

This paper deals with the boundary value problem for the operator Sturm-Liouville type D²=D²(h, H, q₁,q₂,τ,φ) generated by-y''(x)+∑ᵢ₌₁²qᵢ(x)y(x-iτ)=λ y(x),\,x∈[0, π]y'(0)-hy(0)=0,\, y'(π)+Hy(π)=0where π/3≤ τ <π/2,\,\,h, H∈ R\0\ and λ is a spectral parameter. We assume that qᵢ, $i=1,2$ are real-valued potential functions from L₂ [0, π]. We establish a formula for the first regularized trace of this operator. 2020 Mathematics Subject Classification. 34B09, 34B24, 34L10