On the Essential Spectrum of Schrödinger Operators on Trees

Jonathan Breuer*, Sergey Denisov, Latif Eliaz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


It is known that the essential spectrum of a Schrödinger operator H on ℓ2(ℕ) is equal to the union of the spectra of right limits of H. The natural generalization of this relation to ℤn is known to hold as well. In this paper we generalize the notion of right limits to general infinite connected graphs and construct examples of graphs for which the essential spectrum of the Laplacian is strictly bigger than the union of the spectra of its right limits. As these right limits are trees, this result is complemented by the fact that the equality still holds for general bounded operators on regular trees. We prove this and characterize the essential spectrum in the spherically symmetric case.

Original languageAmerican English
Article number33
JournalMathematical Physics Analysis and Geometry
Issue number4
StatePublished - 1 Dec 2018

Bibliographical note

Publisher Copyright:
© 2018, Springer Nature B.V.


  • Essential spectrum
  • Graph Laplacian
  • Right limits
  • Schrödinger operators


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