Pré-Publication, Document De Travail Année : 2024

ENGINEERING SSF WITH SINGULARITIES FOR SELF-ADJOINT OPERATORS ON THE LATTICE

Résumé

We analyze the properties of the spectral shift function (SSF) for some dispersive self-adjoint operators under suitable compact perturbations. New mechanisms allowing the SSF to have singularities at the thresholds are exhibited, based on the degeneracy of the spectrum of the unperturbed operator. In particular, we show how any desired type of singularities can be engineered in this situation. These results are completed by Levinson type results.

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Dates et versions

hal-04713420 , version 1 (29-09-2024)
hal-04713420 , version 2 (23-10-2025)

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Marouane Assal, Olivier Bourget, Diomba Sambou, Amal Taarabt. ENGINEERING SSF WITH SINGULARITIES FOR SELF-ADJOINT OPERATORS ON THE LATTICE. 2024. ⟨hal-04713420v1⟩
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