Regularized Traces of Singular Differential Operators with Canonical Boundary Conditions / Kozko A.I., Pechentsov A.S. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 4. P. 11-17 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

A self-adjoint differential operator L of order 2m is considered in L₂[0,∞) with the classic boundary conditions

y^(k₁)(0) = y^(k₂)(0) = y^(k₃)(0) = ... = y^(k_m)(0) = 0, where 0 ≤ k₁ < k₂ < ... < k_m ≤ 2m-1 and {k_s}_s=1^m ∪ {2m-1-k_s}_s=1^m = {0,1,2,... ,2m-1}. The operator L is perturbed by the operator of multiplication by a real measurable bounded function q(x) with a compact support: Pf(x) = q(x)f(x),  f∈L₂[0,∞). The regularized trace of the operator L+P is calculated.

Key words: regularized traces, spectral function, eigenvalues, self-adjoint extension, singular differential operators.