Trace formulas for Schrödinger operators on periodic graphs

Evgeny Korotyaev, Наталья Сабурова

Результат исследований: Научные публикации в периодических изданияхстатьярецензирование

1 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаанглийский
Номер статьи125888
ЖурналJournal of Mathematical Analysis and Applications
Том508
Номер выпуска2
DOI
СостояниеОпубликовано - 15 апр 2022

Предметные области Scopus

  • Анализ
  • Прикладная математика

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