Regularized Traces of Higher-Order Singular Differential Operators

We consider singular differential operators of order $2m$, $m\in\mathbb N$, with discrete spectrum in $L_2[0,+\infty)$. For self-adjoint extensions given by the boundary conditions $y(0)=y''(0)=\dotsb=y^{(2m-2)}(0)=0$ or $y'(0)=y'''(0)=\dotsb=y^{(2m-1)}(0)=0$, we obtain regularized traces. We present the explicit form of the spectral function, which can be used for calculating regularized traces.