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Journal of Mathematical Sciences

, Volume 238, Issue 5, pp 750–761 | Cite as

On Minimal Entire Solutions of the One-Dimensional Difference Schrödinger Equation with the Potential υ(z) = e−2πiz

  • A. A. FedotovEmail author
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Let z ∈ ℂ be a complex variable, and let h ∈ (0, 1) and p ∈ ℂ be parameters. For the equation ψ(z + h) + ψ(z − h) + e−2πizψ(z) = 2 cos(2πp)ψ(z), solutions having the minimal possible growth simultaneously as Im z → ∞ and as Im z →  − ∞ are studied. In particular, it is shown that they satisfy one more difference equation ψ(z + 1) + ψ(z − 1) + e−2πiz/hψ(z) = 2 cos(2πp/h)ψ(z).

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.St.Petersburg State UniversitySt. PetersburgRussia

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