Jussi Behrndt, A. F.M. Ter Elst, Fritz Gesztesy

Research output: Contribution to journalArticlepeer-review


We prove a generalized Birman-Schwinger principle in the nonself- adjoint context. In particular, we provide a detailed discussion of geometric and algebraic multiplicities of eigenvalues of the basic operator of interest (e.g., a Schrödinger operator) and the associated Birman-Schwinger operator, and additionally offer a careful study of the associated Jordan chains of generalized eigenvectors of both operators. In the course of our analysis we also study algebraic and geometric multiplicities of zeros of strongly analytic operatorvalued functions and the associated Jordan chains of generalized eigenvectors. We also relate algebraic multiplicities to the notion of the index of analytic operator-valued functions and derive a general Weinstein-Aronszajn formula for a pair of non-self-adjoint operators.

Original languageEnglish
Pages (from-to)799-845
Number of pages47
JournalTransactions of the American Mathematical Society
Issue number2
Publication statusPublished - 2022


  • Algebraic and geometric multiplicities
  • Birman-Schwinger principle
  • Jordan chains
  • The index of meromorphic operator-valued functions
  • The Weinstein-Aronszajn formula

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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