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• W2088121945 abstract "We study the manner in which a sequence of spectral shift functions $xi(cdot;H_j,H_{0,j})$ associated with abstract pairs of self-adjoint operators $(H_j, H_{0,j})$ in Hilbert spaces $cH_j$, $jinbbN$, converge to a limiting spectral shift function $xi(cdot;H,H_0)$ associated with a pair $(H,H_0)$ in the limiting Hilbert space $cH$ as $jtoinfty$ (mimicking the infinite volume limit in concrete applications to multi-dimensional Schrodinger operators). Our techniques rely on a Fredholm determinant approach combined with certain measure theoretic facts. In particular, we show that prior vague convergence results for spectral shift functions in the literature actually extend to the notion of weak convergence. More precisely, in the concrete case of multi-dimensional Schrodinger operators on a sequence of domains $Omega_j$ exhausting $bbR^n$ as $jtoinfty$, we extend the convergence of associated spectral shift functions from vague to weak convergence and also from Dirichlet boundary conditions to more general self-adjoint boundary conditions on $partialOmega_j$." @default.
• W2088121945 created "2016-06-24" @default.
• W2088121945 creator A5053434924 @default.
• W2088121945 creator A5075830285 @default.
• W2088121945 date "2011-11-01" @default.
• W2088121945 modified "2023-09-27" @default.
• W2088121945 title "An Abstract Approach to Weak Convergence of Spectral Shift Functions and Applications to Multi-Dimensional Schrodinger Operators" @default.
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• W2088121945 hasPublicationYear "2011" @default.
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