dc.contributor.author | Antonelli, Gioacchino | |
dc.contributor.author | Le Donne, Enrico | |
dc.date.accessioned | 2022-03-03T08:25:07Z | |
dc.date.available | 2022-03-03T08:25:07Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | Antonelli, G., & Le Donne, E. (2022). Polynomial and horizontally polynomial functions on Lie groups. <i>Annali di Matematica Pura ed Applicata</i>, <i>201</i>(5), 2063-2100. <a href="https://doi.org/10.1007/s10231-022-01192-z" target="_blank">https://doi.org/10.1007/s10231-022-01192-z</a> | |
dc.identifier.other | CONVID_104476894 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/80056 | |
dc.description.abstract | We generalize both the notion of polynomial functions on Lie groups and the notion of horizontally affine maps on Carnot groups. We fix a subset S of the algebra g of left-invariant vector fields on a Lie group G and we assume that S Lie generates g. We say that a function f:G→R (or more generally a distribution on G) is S-polynomial if for all X∈S there exists k∈N such that the iterated derivative Xkf is zero in the sense of distributions. First, we show that all S-polynomial functions (as well as distributions) are represented by analytic functions and, if the exponent k in the previous definition is independent on X∈S, they form a finite-dimensional vector space. Second, if G is connected and nilpotent, we show that S-polynomial functions are polynomial functions in the sense of Leibman. The same result may not be true for non-nilpotent groups. Finally, we show that in connected nilpotent Lie groups, being polynomial in the sense of Leibman, being a polynomial in exponential chart, and the vanishing of mixed derivatives of some fixed degree along directions of g are equivalent notions. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | Springer | |
dc.relation.ispartofseries | Annali di Matematica Pura ed Applicata | |
dc.rights | CC BY 4.0 | |
dc.subject.other | nilpotent Lie groups | |
dc.subject.other | polynomial maps | |
dc.subject.other | Leibman Polynomial | |
dc.subject.other | polynomial on groups | |
dc.subject.other | horizontally affine functions | |
dc.subject.other | precisely monotone sets | |
dc.title | Polynomial and horizontally polynomial functions on Lie groups | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202203031771 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | en |
dc.contributor.oppiaine | Geometrinen analyysi ja matemaattinen fysiikka | fi |
dc.contributor.oppiaine | Matematiikka | fi |
dc.contributor.oppiaine | Analyysin ja dynamiikan tutkimuksen huippuyksikkö | fi |
dc.contributor.oppiaine | Geometric Analysis and Mathematical Physics | en |
dc.contributor.oppiaine | Mathematics | en |
dc.contributor.oppiaine | Analysis and Dynamics Research (Centre of Excellence) | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 2063-2100 | |
dc.relation.issn | 0373-3114 | |
dc.relation.numberinseries | 5 | |
dc.relation.volume | 201 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © The Author(s) 2022 | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 713998 | |
dc.relation.grantnumber | 713998 | |
dc.relation.grantnumber | 322898 | |
dc.relation.grantnumber | 288501 | |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/713998/EU//GeoMeG | |
dc.subject.yso | polynomit | |
dc.subject.yso | harmoninen analyysi | |
dc.subject.yso | ryhmäteoria | |
dc.subject.yso | differentiaaligeometria | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p17241 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p28124 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p12497 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p16682 | |
dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |
dc.relation.doi | 10.1007/s10231-022-01192-z | |
dc.relation.funder | European Commission | en |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Euroopan komissio | fi |
dc.relation.funder | Suomen Akatemia | fi |
dc.relation.funder | Suomen Akatemia | fi |
jyx.fundingprogram | ERC Starting Grant | en |
jyx.fundingprogram | Academy Project, AoF | en |
jyx.fundingprogram | Academy Research Fellow, AoF | en |
jyx.fundingprogram | ERC Starting Grant | fi |
jyx.fundingprogram | Akatemiahanke, SA | fi |
jyx.fundingprogram | Akatemiatutkija, SA | fi |
jyx.fundinginformation | G.A. was partially supported by the European Research Council (ERC Starting Grant 713998 GeoMeG ‘Geometry of Metric Groups’). E.L.D. was partially supported by the Academy of Finland (grant 288501 ‘Geometry of subRiemannian groups’ and by grant 322898 ‘Sub-Riemannian Geometry via Metric-geometry and Lie-group Theory’) and by the European Research Council (ERC Starting Grant 713998 GeoMeG ‘Geometry of Metric Groups’) | |
dc.type.okm | A1 | |