On the Koplienko spectral shift function, I. Basics

zbMath1190.47016arXiv0705.3629MaRDI QIDQ3535066

Alexander Pushnitski, Barry Simon, Friedrich Gesztesy

Publication date: 10 November 2008

Full work available at URL: https://arxiv.org/abs/0705.3629

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Spectrum, resolvent (47A10) General spectral theory of ordinary differential operators (34L05) Perturbation theory of linear operators (47A55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Quantum scattering theory (81U99)

Related Items (19)

Trace formulas for additive and non-additive perturbations ⋮ Trace Formulas for Schrödinger Operators in Connection with Scattering Theory for Finite-gap Backgrounds ⋮ The Spectral Shift Function and the Witten Index ⋮ Higher order spectral shift ⋮ An asymptotic formula concerning the eigenvalues of the Dirichlet Laplacian in a planar domain ⋮ Estimates and trace formulas for unitary and resolvent comparable perturbations ⋮ Spectral shift function of higher order ⋮ On the Witten index in terms of spectral shift functions ⋮ Trace formulae for perturbations of class \(s_m\) ⋮ Koplienko trace formula ⋮ Higher-order spectral shift for pairs of contractions via multiplicative path ⋮ On the Arazy conjecture concerning Schur multipliers on Schatten ideals ⋮ Koplienko spectral shift function on the unit circle ⋮ Trace formulas for resolvent comparable operators ⋮ The Koplienko-Neidhardt trace formula for unitaries -- a new proof ⋮ Third order trace formula ⋮ Trace class conditions for functions of Schrödinger operators ⋮ Dependence of the density of states on the probability distribution. II: Schrödinger operators on \(\pmb{\mathbb{R}}^d\) and non-compactly supported probability measures ⋮ Resolution of Peller's problem concerning Koplienko–Neidhardt trace formulae

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