Geodesic
Regularized Traces of Higher-Order Singular Differential Operators
Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 39-49

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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.
Keywords: singular differential operator, regularized trace, Hilbert space, spectral function, self-adjoint extension, Green function.
Mots-clés : Sturm–Liouville problem 
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     title = {Regularized {Traces} of {Higher-Order} {Singular} {Differential} {Operators}},
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A. I. Kozko; A. S. Pechentsov. Regularized Traces of Higher-Order Singular Differential Operators. Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 39-49. http://geodesic.mathdoc.fr/item/MZM_2008_83_1_a4/