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- W2227611334 abstract "We study perturbations of a self-adjoint positive operator $T$, provided that a perturbation operator $B$ satisfies local subordinate condition $|Bvarphi_k|leqslant bmu_k^{beta}$ with some $beta 0$. Here ${varphi_k}_{k=1}^infty$ is an orthonormal system of the eigenvectors of the operator $T$ corresponding to the eigenvalues ${mu_k}_{k=1}^infty$. We introduce the concept of $alpha$-non-condensing sequence and prove the theorem on the comparison of the eigenvalue-counting functions of the operators $T$ and $T+B$. Namely, it is shown that if ${mu_k}$ is $alpha-$non-condensing then the difference of the eigenvalue-counting functions is subject to relation $$|n(r,, T)- n(r,, T+B)| leqslant C[n(r+ar^gamma,, T) - n(r-ar^gamma,, T)] +C_1 $$ with some constants $C, C_1, a$ and $gamma = max(0, beta, 2beta+alpha-1)in [0,1)$." @default.
- W2227611334 created "2016-06-24" @default.
- W2227611334 creator A5076625726 @default.
- W2227611334 date "2012-02-23" @default.
- W2227611334 modified "2023-09-27" @default.
- W2227611334 title "Eigenvalue Asymptotics of Perturbed Self-adjoint Operators" @default.
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