Reconstruction of Solutions to Abstract Schrödinger, Diffusion, and Wave-type Equations From Snapshots
Year: 2026
Type: preprint
Abstract: It is shown that if one knows "sufficiently many" snapshots (samples) from an individual solution of a Schrödinger-type equation-which is bandlimited in an appropriate sense-then the solution can be reconstructed by a simple formula similar to the Shannon formula for bandlimited signals. Furthermore, results demonstrate that by using snapshots of bandlimited solutions of a Schrödinger-type equation, one can reconstruct bandlimited solutions of some relevant diffusion- and wave-type equations. Interestingly, the reconstruction formulas are essentially independent of the operators defining the equations.
Source: arXiv (Cornell University)
Author: Isaac Z Pesenson
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204898332