{"paper":{"title":"Multifractal analysis of Bernoulli convolutions associated with Salem numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.CA","authors_text":"De-Jun Feng","submitted_at":"2011-11-10T08:16:54Z","abstract_excerpt":"We consider the multifractal structure of the Bernoulli convolution $\\nu_{\\lambda}$, where $\\lambda^{-1}$ is a Salem number in $(1,2)$. Let $\\tau(q)$ denote the $L^q$ spectrum of $\\nu_\\lambda$. We show that if $\\alpha \\in [\\tau'(+\\infty), \\tau'(0+)]$, then the level set $$E(\\alpha):={x\\in \\R:\\; \\lim_{r\\to 0}\\frac{\\log \\nu_\\lambda([x-r, x+r])}{\\log r}=\\alpha}$$ is non-empty and $\\dim_HE(\\alpha)=\\tau^*(\\alpha)$, where $\\tau^*$ denotes the Legendre transform of $\\tau$. This result extends to all self-conformal measures satisfying the asymptotically weak separation condition. We point out that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2414","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"}