We consider Schrödinger operators with periodic potentials on periodic discrete graphs. Their spectrum consists of a finite number of bands. We determine trace formulas for the Schrödinger operators. The proof is based on the decomposition of the Schrödinger operators into a direct integral and a specific representation of fiber operators. The traces of the fiber operators are expressed as finite Fourier series of the quasimomentum. The coefficients of the Fourier series are given in terms of the potentials and cycles in the quotient graph from some specific cycle sets. We also present the trace formulas for the heat kernel and the resolvent of the Schrödinger operators and the determinant formulas.

Original languageEnglish
Article number125888
JournalJournal of Mathematical Analysis and Applications
Volume508
Issue number2
DOIs
StatePublished - 15 Apr 2022

    Scopus subject areas

  • Analysis
  • Applied Mathematics

    Research areas

  • Discrete Schrödinger operators, Periodic graphs, Trace formulas

ID: 91318467