Fredholm theory of differential operators on periodic graphs

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

The paper is devoted to the Fredholm theory of differential operators on ifinite metric graphs imbedded in ℝn and periodic with respect to a group G isomorphic to Zr, 1 ≤ r ≤ n. It is assumed that the coefficients of differential operators and vertex conditions are not periodic. Necessary and sufficient conditions for operators under consideration to be Fredholm are obtained.

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages173-186
Number of pages14
DOIs
StatePublished - 2018
Externally publishedYes

Publication series

NameContemporary Mathematics
Volume717
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Keywords

  • Essential spectrum
  • Fredholm theory
  • Localization
  • Quantum graphs

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