Вестник Московского Университета. Математика, Механика - Содержание

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. 66, N 4, 2011.].

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(km)(0) = 0,
where 0 ≤ k1 < k2 < ... < km ≤ 2m-1 and {ks}s=1m ∪ {2m-1-ks}s=1m = {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.