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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19956049 |
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Table of Contents:
- <p>We study prescribed density-selected phase drives generated by singular kernels and<br>their regularizations. In bounded-kernel regimes, stability is often formulated in operator<br>norm. For singular kernels, uniform phase control is generally unavailable. We identify<br>the strong operator topology as the stable topology for singular phase-drive limits. After<br>developing admissible phase-convergence mechanisms for regularized singular convolutions<br>Wε ∗ pt → W ∗ pt, we prove strong convergence of one-step imprints, finite prescribed<br>schedules, and continuum product-integral phase drives. We also show that fixed marginals<br>remain stable in trace norm under strong unitary convergence. Finally, we prove an exact<br>operator-norm obstruction: norm convergence of multiplication unitaries is equivalent to L∞-<br>convergence of the corresponding exponential phases. Recovery of operator-norm estimates<br>occurs only in regimes where uniform phase control is restored.</p>