Spectral shift functions and Dirichlet-to-Neumann maps

Jussi Behrndt; Fritz Gesztesy; Shu Nakamura

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arXiv · 1609.08292

Spectral shift functions and Dirichlet-to-Neumann maps

Jussi Behrndt·Fritz Gesztesy·Shu Nakamura

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Abstract

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, Schr\"{o}dinger operators with compactly supported potentials, and finally, Schr\"{o}dinger operators with singular potentials supported on hypersurfaces. 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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BibTeX RIS

Jussi Behrndt, Fritz Gesztesy, Shu Nakamura. 2016-09-27. Spectral shift functions and Dirichlet-to-Neumann maps. https://arxiv.org/abs/1609.08292

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