Regularized traces of singular differential operators with canonical boundary conditions |
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Authors: | A I Kozko A S Pechentsov |
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Institution: | 1.Faculty of Mechanics and Mathematics,Moscow State University,Leninskie Gory, Moscow,Russia |
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Abstract: | A self-adjoint differential operator \(\mathbb{L}\) of order 2m is considered in L 20,∞) with the classic boundary conditions \(y^{(k_1 )} (0) = y^{(k_2 )} (0) = y^{(k_3 )} (0) = \ldots = y^{(k_m )} (0) = 0\), where 0 ≤ k 1 < k 2 < ... < k m ≤ 2m ? 1 and {k s } s=1 m ∪ {2m ? 1 ? k s } s=1 m = {0, 1, 2, ..., 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 ∈ L 20,∞). The regularized trace of the operator \(\mathbb{L} + \mathbb{P}\) is calculated. |
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