Reconstruction of solutions to abstract Schrodinger, diffusion, and wave-type equations from snapshots

Isaac Z. Pesenson

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arXiv · 2609.21915

Reconstruction of solutions to abstract Schrodinger, diffusion, and wave-type equations from snapshots

Isaac Z. Pesenson

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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.

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Isaac Z. Pesenson. 2026-09-18. Reconstruction of solutions to abstract Schrodinger, diffusion, and wave-type equations from snapshots. https://arxiv.org/abs/2609.21915

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