Regularized traces of singular differential operators with canonical boundary conditions

A. I. Kozko   ; A. S. Pechentsov

Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2011), pp. 11-17

Résumé

A self-adjoint differential operator $\mathbb L$ of order $2m$ is considered in $L_2[0,\infty)$ with classic boundary conditions $y^{(k_1)}(0)=y^{(k_2)}(0)=y^{(k_3)}(0)=\ldots =y^{(k_m)}(0)=0$, where $0\le k_1< k_2< \ldots < k_m\le 2m-1$ and $\{k_s\}_{s=1}^{m}\cup \{2m-1-k_s\}_{s=1}^{m}=\{0,1,2,\dots ,2m-1\}$. The operator $\mathbb L$ is perturbed by the operator of multiplication by a real measurable bounded function $q(x)$ with a compact support: $\mathbb{P}f(x)=q(x)f(x)$, $f\in L_2[0,\infty )$. The regularized trace of the operator $\mathbb{L}+\mathbb{P}$ is calculated.