On the Point Spectrum of Self-Adjoint Operators That Appears under Singular Perturbations of Finite Rank |
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Authors: | Dudkin M E Koshmanenko V D |
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Institution: | (1) Kiev Polytechnic Institute, Kiev;(2) Institute of Mathematics, Ukrainian Academy of Sciences, Kiev |
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Abstract: | We discuss purely singular finite-rank perturbations of a self-adjoint operator A in a Hilbert space . The perturbed operators
are defined by the Krein resolvent formula
, Im z 0, where B
z are finite-rank operators such that dom B
z dom A = |0}. For an arbitrary system of orthonormal vectors
satisfying the condition span |
i
} dom A = |0} and an arbitrary collection of real numbers
, we construct an operator
that solves the eigenvalue problem
. We prove the uniqueness of
under the condition that rank B
z = n. |
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Keywords: | |
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