Spectral theory of discontinuous functions of self-adjoint operators: Essential spectrum

DOI10.1007/s00020-010-1789-4zbMath1198.47016arXiv0907.3370OpenAlexW2043084937MaRDI QIDQ601712

Alexander Pushnitski

Publication date: 29 October 2010

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.3370

zbMATH Keywords

essential spectrumscattering matrixspectral projections

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of partial differential operators (47F05) Scattering theory of linear operators (47A40)

Related Items (5)

On a generalisation of Krein's example ⋮ The Birman-Schwinger principle on the essential spectrum ⋮ Spectral action beyond the weak-field approximation ⋮ Trace class conditions for functions of Schrödinger operators ⋮ On the difference of spectral projections

Cites Work

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• The Birman-Schwinger principle on the essential spectrum
• Spectral properties of the abstract scattering matrix
• Functions of operators under perturbations of class \(S_p\)
• Spectral theory of discontinuous functions of self-adjoint operators and scattering theory
• Hankel operators in the perturbation theory of unitary and self-adjoint operators
• The index of a pair of projections
• Double operator integrals in a Hilbert space
• Lipschitz functions of perturbed operators
• Wave operators and similarity for some non-selfadjoint operators
• Schrödinger semigroups
• On Krein’s example
• The scattering matrix and the differences of spectral projections
• Two Subspaces
• The spectral shift function and the invariance principle

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