An abstract approach to weak convergence of spectral shift functions and applications to multi-dimensional Schrödinger operators

DOI10.4171/JST/28zbMath1263.47015arXiv1111.0096OpenAlexW2964079195MaRDI QIDQ442468

Roger A. Nichols, Friedrich Gesztesy

Publication date: 11 August 2012

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.0096

zbMATH Keywords

weak convergenceSchrödinger operatorsFredholm determinantsspectral shift functions

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Scattering theory for PDEs (35P25) Applications of operator theory in the physical sciences (47N50) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) General theory of ordinary differential operators (47E05) General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10) Scattering theory of linear operators (47A40)

Related Items (6)

Effective computation of traces, determinants, and \(\zeta\)-functions for Sturm-Liouville operators ⋮ The spectral shift function and the Friedel sum rule ⋮ Spectral shift functions and Dirichlet-to-Neumann maps ⋮ On the index of a non-Fredholm model operator ⋮ On an integral formula for Fredholm determinants related to pairs of spectral projections ⋮ On index theory for non-Fredholm operators: A (1 + 1)-dimensional example

Cites Work

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• On the theory of linear equations and Fredholm determinants
• Measure and integration theory. Transl. from the German by Robert B. Burckel
• Continuity of eigenvalues for Schrödinger operators, \(L^p\)-properties of Kato type integral operators.

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