Asymptotics and Estimates for the Discrete Spectrum of the Schrodinger Operator ¨ on a Discrete Periodic Graph

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Abstract

The periodic Schr¨odinger operator H on a discrete periodic graph is treated. The discrete spectrum is estimated for the perturbed operator H±(t) = H±tV, t > 0, where V ≥ 0 is a decaying potential. In the case when the potential has a power asymptotics at infinity, an asymptotics is obtained for the discrete spectrum of the operator H±(t) for a large coupling constant

Original languageEnglish
Pages (from-to)9-29
Number of pages21
JournalSt. Petersburg Mathematical Journal
Volume32
Issue number1
DOIs
StatePublished - 11 Jan 2021

Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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