A Formula for Time-to-Frequency Wave Boundary Data Conversion by the Boundary Control Method
Year: 2026
Type: preprint
Abstract: Given the wave equation on a compact Riemannian manifold with boundary, we derive an explicit reconstruction procedure to represent the frequency-domain Neumann-to-Dirichlet map in terms of the time-domain Neumann-to-Dirichlet map at any non-eigenfrequency. If the wave equation is exactly controllable, we derive an explicit formula to compute the former from the latter. The derivation is based on the boundary control method and requires only knowledge on the boundary of the manifold. The formula is stable when the level of regularization is fixed. The numerical feasibility is validated using one-dimensional examples in both Euclidean and non-Euclidean geometries.
Source: arXiv (Cornell University)
Author: Yang, Yang
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7129487464
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