{"paper":{"title":"On perturbations of the isometric semigroup of shifts on the semiaxis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"A.D. Baranov, G.G. Amosov, V.V. Kapustin","submitted_at":"2012-09-15T21:02:51Z","abstract_excerpt":"We study perturbations $(\\tilde\\tau_t)_{t\\ge 0}$ of the semigroup of shifts $(\\tau_t)_{t\\ge 0}$ on $L^2(\\R_+)$ with the property that $\\tilde\\tau_t - \\tau_t$ belongs to a certain Schatten-von Neumann class $\\gS_p$ with $p\\ge 1$. We show that, for the unitary component in the Wold-Kolmogorov decomposition of the cogenerator of the semigroup $(\\tilde\\tau_t)_{t\\ge 0}$, {\\it any singular} spectral type may be achieved by $\\gS_1$ perturbations. We provide an explicit construction for a perturbation with a given spectral type based on the theory of model spaces of the Hardy space $H^2$. Also we show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3434","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}