Approximately Dual and Pseudo-Dual Probabilistic Frames
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914570138812416 |
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| author | Chen, Dongwei King, Emily J. Shonkwiler, Clayton |
| author_facet | Chen, Dongwei King, Emily J. Shonkwiler, Clayton |
| contents | This paper studies properties of dual probabilistic frames -- in particular in relation to redundancy -- and introduces both approximately dual probabilistic frames and pseudo-dual probabilistic frames. We show that the canonical dual probabilistic frame is the only dual frame of pushforward type of a probabilistic frame with zero redundancy. Furthermore, we show that probabilistic frames with finite redundancy are atomic and finite. Approximately dual probabilistic frames generalize duality, with pseudo-duality being a further generalization. We introduce these concepts and prove certain structural results. In particular, every probabilistic frame has a discrete finite frame as an approximate dual. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximately Dual and Pseudo-Dual Probabilistic Frames Chen, Dongwei King, Emily J. Shonkwiler, Clayton Functional Analysis 42C15 This paper studies properties of dual probabilistic frames -- in particular in relation to redundancy -- and introduces both approximately dual probabilistic frames and pseudo-dual probabilistic frames. We show that the canonical dual probabilistic frame is the only dual frame of pushforward type of a probabilistic frame with zero redundancy. Furthermore, we show that probabilistic frames with finite redundancy are atomic and finite. Approximately dual probabilistic frames generalize duality, with pseudo-duality being a further generalization. We introduce these concepts and prove certain structural results. In particular, every probabilistic frame has a discrete finite frame as an approximate dual. |
| title | Approximately Dual and Pseudo-Dual Probabilistic Frames |
| topic | Functional Analysis 42C15 |
| url | https://arxiv.org/abs/2505.13885 |