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Asymptotic observable symmetry for spacetime observability of waves I: The disc
Abstract
Building on the spacetime observable symmetry discovered in NWX (2025), we introduce asymptotic observable symmetry (AOS) for the wave equation. Its central object is a family of generated approximate velocities constructed from fixed profiles, carrying the same propagation-induced symmetry at different scales and asymptotically realized by exact waves. We investigate AOS on the disc through radial propagation and reflection. This gives a family of spacetime measurable observation sets satisfying the essential spacetime measurable geometric control condition for a fixed positive observation time. However, the observability inequality fails on each of these fixed sets.
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BibTeX
@misc{xiang2026asymptotic,
title = {{Asymptotic observable symmetry for spacetime observability of waves I: The disc}},
author = {Shengquan Xiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31477},
eprint = {2610.31477},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31477},
}
RIS
TY - UNPB
TI - Asymptotic observable symmetry for spacetime observability of waves I: The disc
AU - Shengquan Xiang
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31477
UR - https://arxiv.org/abs/2610.31477
AB - Building on the spacetime observable symmetry discovered in NWX (2025), we introduce asymptotic observable symmetry (AOS) for the wave equation. Its central object is a family of generated approximate velocities constructed from fixed profiles, carrying the same propagation-induced symmetry at different scales and asymptotically realized by exact waves. We investigate AOS on the disc through radial propagation and reflection. This gives a family of spacetime measurable observation sets satisfying the essential spacetime measurable geometric control condition for a fixed positive observation time. However, the observability inequality fails on each of these fixed sets.
ER -