Frames for source recovery from non-uniform dynamical samples
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911581928947712 |
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| author | Ruchi Vashisht, Lalit Kumar |
| author_facet | Ruchi Vashisht, Lalit Kumar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frames for source recovery from non-uniform dynamical samples Ruchi Vashisht, Lalit Kumar Functional Analysis 93B30, 42C15, 42C30 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. |
| title | Frames for source recovery from non-uniform dynamical samples |
| topic | Functional Analysis 93B30, 42C15, 42C30 |
| url | https://arxiv.org/abs/2501.16949 |