Frames for source recovery from non-uniform dynamical samples

Let [Formula: see text] be a fixed positive integer, and let [Formula: see text] be a fixed odd integer coprime with [Formula: see text] such that [Formula: see text]. We investigate the stable recovery of the source term of the discrete dynamical system indexing over the non-uniform discrete set [Formula: see text] considered by Gabardo and Nashed in the context of one dimensional spectral pairs for infinite-dimensional separable Hilbert spaces. This is inspired by recent work due to Aldroubi et al. on stable recovery of source terms in dynamical systems. Extending results due to Aldroubi et al., first, we give a necessary and sufficient condition for the stable recovery of the source term in finitely many iterations. Afterward, we derive a necessary condition for the stable recovery 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 stable recovery of the source term in infinitely many iterations.