Sep 27, 2016
Spectral shift functions and Dirichlet-to-Neumann maps
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The spectral shift function of a pair of self-adjoint operators is expressed<br />
via an abstract operator valued Titchmarsh--Weyl $m$-function. This general<br />
result is applied to different self-adjoint realizations of second-order<br />
elliptic partial differential operators on smooth domains with compact<br />
boundaries, Schr\"{o}dinger operators with compactly supported potentials, and<br />
finally, Schr\"{o}dinger operators with singular potentials supported on<br />
hypersurfaces. In these applications the spectral shift function is determined<br />
in an explicit form with the help of (energy parameter dependent)<br />
Dirichlet-to-Neumann maps.
via an abstract operator valued Titchmarsh--Weyl $m$-function. This general<br />
result is applied to different self-adjoint realizations of second-order<br />
elliptic partial differential operators on smooth domains with compact<br />
boundaries, Schr\"{o}dinger operators with compactly supported potentials, and<br />
finally, Schr\"{o}dinger operators with singular potentials supported on<br />
hypersurfaces. In these applications the spectral shift function is determined<br />
in an explicit form with the help of (energy parameter dependent)<br />
Dirichlet-to-Neumann maps.
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- arXiv ID : arXiv:1609.08292