Introduces approximately dual and pseudo-dual probabilistic frames, proves the canonical dual is the unique pushforward-type dual for zero-redundancy cases, shows finite-redundancy frames are atomic and finite, and establishes that every probabilistic frame has a discrete finite approximate dual.
Applied and Numerical Harmonic Analysis
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Approximately Dual and Pseudo-Dual Probabilistic Frames
Introduces approximately dual and pseudo-dual probabilistic frames, proves the canonical dual is the unique pushforward-type dual for zero-redundancy cases, shows finite-redundancy frames are atomic and finite, and establishes that every probabilistic frame has a discrete finite approximate dual.