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- W1509484927 abstract "We use Rokhlin's Theorem on the uniqueness of canonical systems to find a new way to establish connections between Function Theory in the unit disk and rank one perturbations of self-adjoint or unitary operators. In the n-dimensional case, we prove that for any cyclic self-adjoint operator $A$, operator $A_lambda= A + Sigma_{k=1}^n lambda_k(cdot,phi_k)phi_k$ is pure point for a. e. $lambda=(lambda_1,lambda_2,...,lambda_n) inBbb R^n$ iff operator $A_eta=A+eta(cdot,phi_k)phi_k$ is pure point for a.e. $etainBbb R$ for $k=1,2,...,n$. We also show that if $A_lambda$ is pure point for a.e. $lambdain Bbb R^n$ then $A_lambda$ is pure point for a.e. $lambdain gamma$ for any analytic curve $gammainBbb R^n$." @default.
- W1509484927 created "2016-06-24" @default.
- W1509484927 creator A5053068048 @default.
- W1509484927 date "1996-06-24" @default.
- W1509484927 modified "2023-09-27" @default.
- W1509484927 title "Canonical systems and finite rank perturbations of spectra" @default.
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