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This article is cited in 2 scientific papers (total in 2 papers)
On Spectral Properties of the Discrete Schrödinger Operator with Pure Imaginary Finite Potential
M. M. Faddeev Saint-Petersburg State University
Abstract:
In this paper, we consider the spectral properties of the discrete Schrödinger operator in the space of square integrable two-sided sequences with a pure imaginary potential of finite rank with zero mean value. We show that if such potentials are small, then the spectrum of the operator under study coincides with the spectrum of the unperturbed operator, and the operator itself is similar to a self-adjoint operator.
Keywords:
discrete Schrödinger operator, spectral problem, $\mathscr{PT}$-symmetric potential, similarity to a self-adjoint operator.
Received: 27.02.2008
Citation:
M. M. Faddeev, “On Spectral Properties of the Discrete Schrödinger Operator with Pure Imaginary Finite Potential”, Mat. Zametki, 85:3 (2009), 451–455; Math. Notes, 85:3 (2009), 437–440
Linking options:
https://www.mathnet.ru/eng/mzm4670https://doi.org/10.4213/mzm4670 https://www.mathnet.ru/eng/mzm/v85/i3/p451
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