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arXiv · 2501.16949

Frames for source recovery from non-uniform dynamical samples

Ruchi·Lalit Kumar Vashisht
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Abstract

Motivated by the work of Aldroubi et al., we investigate the stability of the source term of the discrete dynamical system indexing over a non-uniform discrete set arising from spectral pairs in infinite-dimensional separable Hilbert spaces. Extending results due to Aldroubi et al., firstly, we give a necessary and sufficient condition for the recovery of the source term in finitely many iterations. Afterwards, we derive a necessary condition for the stability of the source term in finitely many iterations when it belongs to the closed subspace of an infinite-dimensional separable Hilbert space. Finally, we give a necessary and sufficient condition for the recovery of the source term in infinitely many iterations.

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Ruchi, Lalit Kumar Vashisht. 2025-01-28. Frames for source recovery from non-uniform dynamical samples. https://doi.org/10.1142/s0219691325500456

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