Jordan chains of elliptic partial differential operators and Dirichlet-to-Neumann maps

Tom ter Elst, Jussi Behrndt

Research output: Contribution to journalArticlepeer-review


Let Ω Rd be a bounded open set with Lipschitz boundary Γ. It will be shown that the Jordan chains of m-sectorial second-order elliptic partial differential operators with measurable coefficients and (local or non-local) Robin boundary conditions in L2.Ω/ can be characterized with the help of Jordan chains of the Dirichlet-to-Neumann map and the boundary operator from H1=2.Γ/ into H-1=2. Γ/. This result extends the Birman-Schwinger principle in the framework of elliptic operators for the characterization of eigenvalues, eigenfunctions and geometric eigenspaces to the complete set of all generalized eigenfunctions and algebraic eigenspaces.

Original languageEnglish
Pages (from-to)1081-1105
Number of pages25
JournalJournal of Spectral Theory
Issue number3
Publication statusPublished - 2021


  • Dirichlet-to-Neumann operator
  • Eigenvector
  • Generalized eigenvector
  • Jordan chain
  • Robin boundary condition

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Geometry and Topology
  • Mathematical Physics


Dive into the research topics of 'Jordan chains of elliptic partial differential operators and Dirichlet-to-Neumann maps'. Together they form a unique fingerprint.

Cite this