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arXiv · 2505.13885

Approximately Dual and Pseudo-Dual Probabilistic Frames

Dongwei Chen·Emily J. King·Clayton Shonkwiler
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Abstract

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.

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Dongwei Chen, Emily J. King, Clayton Shonkwiler. 2025-05-20. Approximately Dual and Pseudo-Dual Probabilistic Frames. https://doi.org/10.1016/j.acha.2026.101885

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