{"paper":{"title":"The Beurling--Malliavin Multiplier Theorem and its analogs for the de Branges spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Victor Havin, Yurii Belov","submitted_at":"2013-09-27T06:44:32Z","abstract_excerpt":"Let $\\omega$ be a non-negative function on $\\mathbb{R}$. We are looking for a non-zero $f$ from a given space of entire functions $X$ satisfying $$(a) \\quad|f|\\leq \\omega\\text{\\quad or\\quad(b)}\\quad |f|\\asymp\\omega.$$ The classical Beurling--Malliavin Multiplier Theorem corresponds to $(a)$ and the classical Paley--Wiener space as $X$. We survey recent results for the case when $X$ is a de Branges space $\\he$. Numerous answers mainly depend on the behaviour of the phase function of the generating function $E$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7130","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"}