Spectral shift functions and Dirichlet-to-Neumann maps

Spectral shift functions and Dirichlet-to-Neumann maps

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 bound...

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Bibliographic Details
Published in:Mathematische annalen Vol. 371; no. 3-4; pp. 1255 - 1300
Main Authors: Behrndt, Jussi, Gesztesy, Fritz, Nakamura, Shu
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 2018
Springer Nature B.V
Subjects:
Differential equations
Dirichlet problem
Mathematics
Mathematics and Statistics
Operators (mathematics)
Spectra
Primary 35J10
47B25
Secondary 35P20
35P25
47A55
47B10
35J15
47A10
81Q10
47A40
47F05
Online Access:Get full text
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Summary: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.
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content type line 23
Communicated by Y. Giga.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-017-1593-4