2026/03/31 by Anton Alexa
Engineering · Mathematics · Physics and Astronomy · #Control and Stability of Dynamical Systems #Quantum many-body systems #Spectral Theory in Mathematical Physics #math.FA #math.OA #math.SP #msc:47A10 #msc:47B02 #msc:47D06 #msc:93B30
paper · pdf · doi:10.1007/s11785-026-02016-1
published as Complex Analysis and Operator Theory 20, 154 (2026) · 20 pages. Published in Complex Analysis and Operator Theory
openalex publication_date 2026/07/29 · arxiv created 2026/07/30 · openalex created_date 2026/07/30 · arxiv updated 2026/07/31 · openalex updated_date 2026/08/02
We study rigidity phenomena for time-scaled intertwining families of dissipative semigroups \mathcal Si(t)=e-tAi and prove that a network of bounded injective operators satisfying Kij\mathcal Sj(t)=\mathcal Si(λijt)Kij and Kik=KijKjk necessarily admits a multiplicative gauge representation λij=τi/τj, if and only if the renormalized generators \τiAi\ form a common isospectral class with matching eigenspace dimensions; in particular, eigenspaces are transported isomorphically across sectors. The operators Kij define parallel transport in a flat Hilbert bundle over the index network, with flatness derived from the intertwining constraints rather than assumed. As an application, the mixture observable M(t)=∑i wi\mathcal B0K0i\mathcal Si(t)ψi reduces under finite spectral support to a structured exponential sum. Under spectral separation, the modal parameters are uniquely identifiable, with sector tags determined intrinsically by the operator spectra; under eigenspace observability, active state components are uniquely recovered. Finite-window exact reconstruction holds from 2L samples, and the stability bound ‖\widehatΘ-Θ_∗‖\mathcal X≤ Cstabκexpε follows with constants explicitly controlled by the spectral geometry and observability of the network.