• Corpus ID: 253553130

Higher-order spectral shift function for resolvent comparable perturbations

@inproceedings{Nuland2022HigherorderSS,
  title={Higher-order spectral shift function for resolvent comparable perturbations},
  author={Teun D.H. van Nuland and Anna Skripka},
  year={2022}
}

• T. V. Nuland, A. Skripka
• Published 7 November 2022
• Mathematics

Given a pair of self-adjoint operators H and V such that V is bounded and ( H + V − i ) − 1 − ( H − i ) − 1 belongs to the Schatten-von Neumann ideal S n , n ≥ 2, of operators on a separable Hilbert space, we establish higher order trace formulas for a broad set of functions f containing several major classes of test functions and also establish existence of the respective locally integrable real-valued spectral shift functions determined uniquely up to a low degree polynomial summand. Our result generalizes the result of [14] for Schatten-von Neumman perturbations V and settles earlier attempts to encompass general perturbations with Schatten-von Neumman difference of resolvents, which led to more complicated trace formulas for more restrictive sets of functions f and to analogs of spectral shift functions lacking real-valuedness and/or expected degree of uniqueness. Our proof builds on a general change of variables method derived in this paper and significantly refining those appearing in [11, 15, 16] with respect to several parameters at once.