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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19956049 |
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| _version_ | 1866901386161029120 |
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| author | Panasenko, Dmytro |
| author_facet | Panasenko, Dmytro |
| 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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19956049 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Strong-Topology Limits and Norm Obstructions for Singular Density-Selected Phase Drives Panasenko, Dmytro <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> |
| title | Strong-Topology Limits and Norm Obstructions for Singular Density-Selected Phase Drives |
| url | https://doi.org/10.5281/zenodo.19956049 |