Singular spectral shift is additive
Nurulla Azamov
TL;DR
This paper proves that for trace-class perturbations of self-adjoint operators, the singular part of the spectral shift function adds up when multiple perturbations are combined.
Contribution
It establishes the additivity of the singular spectral shift function for trace-class perturbations, a property not previously confirmed.
Findings
Singular spectral shift function is additive under trace-class perturbations.
Provides a rigorous proof of additivity for the singular part.
Enhances understanding of spectral shift functions in operator theory.
Abstract
In this note it is shown that for trace-class perturbations of self-adjoint operators the singular part of the spectral shift function is additive.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quantum optics and atomic interactions · Quantum chaos and dynamical systems