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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 269, Pages 290–303
(Mi tm2886)
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This article is cited in 28 scientific papers (total in 28 papers)
On the basis property of root vectors of a perturbed self-adjoint operator
A. A. Shkalikov Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
Abstract:
We study perturbations of a self-adjoint operator $T$ with discrete spectrum such that the number of its points on any unit-length interval of the real axis is uniformly bounded. We prove that if $\|B\varphi_n\|\le\mathrm{const}$, where $\varphi_n$ is an orthonormal system of eigenvectors of the operator $T$, then the system of root vectors of the perturbed operator $T+B$ forms a basis with parentheses. We also prove that the eigenvalue-counting functions of $T$ and $T+B$ satisfy the relation $|n(r,T)-n(r,T+B)|\le\mathrm{const}$.
Received in January 2010
Citation:
A. A. Shkalikov, “On the basis property of root vectors of a perturbed self-adjoint operator”, Function theory and differential equations, Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday, Trudy Mat. Inst. Steklova, 269, MAIK Nauka/Interperiodica, Moscow, 2010, 290–303; Proc. Steklov Inst. Math., 269 (2010), 284–298
Linking options:
https://www.mathnet.ru/eng/tm2886 https://www.mathnet.ru/eng/tm/v269/p290
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Abstract page: | 852 | Full-text PDF : | 121 | References: | 189 |
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