Isometric embeddings of snowflakes into finite-dimensional Banach spaces

Le Donne, Enrico; Rajala, Tapio; Walsberg, Erik

doi:10.1090/proc/13778

dc.contributor.author	Le Donne, Enrico
dc.contributor.author	Rajala, Tapio
dc.contributor.author	Walsberg, Erik
dc.date.accessioned	2019-03-18T11:29:04Z
dc.date.available	2019-03-18T11:29:04Z
dc.date.issued	2018
dc.identifier.citation	Le Donne, E., Rajala, T., & Walsberg, E. (2018). Isometric embeddings of snowflakes into finite-dimensional Banach spaces. <i>Proceedings of the American Mathematical Society</i>, <i>146</i>(2), 685-693. <a href="https://doi.org/10.1090/proc/13778" target="_blank">https://doi.org/10.1090/proc/13778</a>
dc.identifier.other	CONVID_27796618
dc.identifier.other	TUTKAID_76244
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/63200
dc.description.abstract	We consider a general notion of snowflake of a metric space by composing the distance with a nontrivial concave function. We prove that a snowflake of a metric space X isometrically embeds into some finite-dimensional normed space if and only if X is finite. In the case of power functions we give a uniform bound on the cardinality of X depending only on the power exponent and the dimension of the vector space.	fi
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	American Mathematical Society
dc.relation.ispartofseries	Proceedings of the American Mathematical Society
dc.rights	CC BY-NC-ND 4.0
dc.subject.other	metriset avaruudet	fi
dc.subject.other	normiavaruudet	fi
dc.subject.other	funktionaalianalyysi	fi
dc.subject.other	fraktaalit	fi
dc.subject.other	metric spaces	fi
dc.subject.other	normed spaces	fi
dc.subject.other	functional analysis	fi
dc.subject.other	fractals	fi
dc.title	Isometric embeddings of snowflakes into finite-dimensional Banach spaces
dc.type	article
dc.identifier.urn	URN:NBN:fi:jyu-201903121827
dc.contributor.laitos	Matematiikan ja tilastotieteen laitos	fi
dc.contributor.laitos	Department of Mathematics and Statistics	en
dc.contributor.oppiaine	Matematiikka	fi
dc.contributor.oppiaine	Mathematics	en
dc.type.uri	http://purl.org/eprint/type/JournalArticle
dc.date.updated	2019-03-12T13:15:17Z
dc.type.coar	http://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatus	peerReviewed
dc.format.pagerange	685-693
dc.relation.issn	0002-9939
dc.relation.numberinseries	2
dc.relation.volume	146
dc.type.version	acceptedVersion
dc.rights.copyright	© 2017 American Mathematical Society
dc.rights.accesslevel	openAccess	fi
dc.relation.grantnumber	288501
dc.relation.grantnumber	274372
dc.subject.yso	funktionaalianalyysi
dc.subject.yso	metriset avaruudet
dc.subject.yso	normiavaruudet
dc.subject.yso	fraktaalit
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p17780
jyx.subject.uri	http://www.yso.fi/onto/yso/p27753
jyx.subject.uri	http://www.yso.fi/onto/yso/p19501
jyx.subject.uri	http://www.yso.fi/onto/yso/p6341
dc.rights.url	https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi	10.1090/proc/13778
dc.relation.funder	Suomen Akatemia	fi
dc.relation.funder	Suomen Akatemia	fi
dc.relation.funder	Academy of Finland	en
dc.relation.funder	Academy of Finland	en
jyx.fundingprogram	Akatemiatutkija, SA	fi
jyx.fundingprogram	Akatemiatutkija, SA	fi
jyx.fundingprogram	Academy Research Fellow, AoF	en
jyx.fundingprogram	Academy Research Fellow, AoF	en
jyx.fundinginformation	The first and second authors acknowledge the support of the Academy of Finland, projects no. 288501 and 274372 The third author acknowledges the support of the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement no. 291111/ MODAG
dc.type.okm	A1