Spectral shift functions and Dirichlet-to-Neumann maps

Jussi Behrndt*, Fritz Gesztesy, Shu Nakamura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator-valued Titchmarsh–Weyl m-function. This general result is applied to different self-adjoint realizations of second-order elliptic partial differential operators on smooth domains with compact boundaries and Schrödinger operators with compactly supported potentials. In these applications the spectral shift function is determined in an explicit form with the help of (energy parameter dependent) Dirichlet-to-Neumann maps.
Original languageEnglish
Pages (from-to)1255-1300
JournalMathematische Annalen
Publication statusPublished - 2018

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