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Article: Bernoulli convolutions associated with certain non-Pisot numbers

TitleBernoulli convolutions associated with certain non-Pisot numbers
Authors
Feng, De JunWang, Yang
KeywordsBernoulli convolutions
Pisot numbers
Random power series
Salem numbers
Self-similar measures
Issue Date2004
Citation
Advances in Mathematics, 2004, v. 187, n. 1, p. 173-194 How to Cite?
DOI: http://dx.doi.org/10.1016/j.aim.2003.05.002
AbstractThe Bernoulli convolution νλ measure is shown to be absolutely continuous with L2 density for almost all 1/2 <λ<1, and singular if λ-1 is a Pisot number. It is an open question whether the Pisot type Bernoulli convolutions are the only singular ones. In this paper, we construct a family of non-Pisot type Bernoulli convolutions νλ such that their density functions, if they exist, are not L2. We also construct other Bernoulli convolutions whose density functions, if they exist, behave rather badly. © 2003 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/363085
ISSN
0001-8708
2023 Impact Factor: 1.5
2023 SCImago Journal Rankings: 2.022

 

DC FieldValueLanguage
dc.contributor.authorFeng, De Jun-
dc.contributor.authorWang, Yang-
dc.date.accessioned2025-10-10T07:44:29Z-
dc.date.available2025-10-10T07:44:29Z-
dc.date.issued2004-
dc.identifier.citationAdvances in Mathematics, 2004, v. 187, n. 1, p. 173-194-
dc.identifier.issn0001-8708-
dc.identifier.urihttp://hdl.handle.net/10722/363085-
dc.description.abstractThe Bernoulli convolution ν<inf>λ</inf> measure is shown to be absolutely continuous with L<sup>2</sup> density for almost all 1/2 <λ<1, and singular if λ<sup>-1</sup> is a Pisot number. It is an open question whether the Pisot type Bernoulli convolutions are the only singular ones. In this paper, we construct a family of non-Pisot type Bernoulli convolutions ν<inf>λ</inf> such that their density functions, if they exist, are not L<sup>2</sup>. We also construct other Bernoulli convolutions whose density functions, if they exist, behave rather badly. © 2003 Elsevier Inc. All rights reserved.-
dc.languageeng-
dc.relation.ispartofAdvances in Mathematics-
dc.subjectBernoulli convolutions-
dc.subjectPisot numbers-
dc.subjectRandom power series-
dc.subjectSalem numbers-
dc.subjectSelf-similar measures-
dc.titleBernoulli convolutions associated with certain non-Pisot numbers-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.aim.2003.05.002-
dc.identifier.scopuseid_2-s2.0-3242877450-
dc.identifier.volume187-
dc.identifier.issue1-
dc.identifier.spage173-
dc.identifier.epage194-

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