Regularized traces of higher-order singular differential operators

Abstract

We consider singular differential operators of order 2m, m ∈ ℕ, with discrete spectrum in L2[0, + ∞). For self-adjoint extensions given by the boundary conditions y(0) = y″(0) = ⋯ = y(2m−2)(0) = 0 or y′(0) = y‴(0) = ⋯ = 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.