Analytic functions and Nash functions along curves

2023
journal article
article
2
dc.abstract.enLet $X$ be a real analytic manifold. A function $f$ : $X \rightarrow \mathbb{R}$ is said to be curve-analytic if it is real analytic when restricted to any locally irreducible real analytic curve in $X$. We prove that every curve-analytic function with subanalytic graph is actually real analytic. To accomplish this task, we give a criterion for an arc-analytic function to be real analytic. A function is called arc-analytic if it is real analytic along any parametric real analytic arc. We also obtain analogous results for Nash manifolds and Nash functions, in which case the assumption of subanalyticity is superfluous.pl
dc.affiliationWydział Matematyki i Informatyki : Instytut Matematykipl
dc.contributor.authorKucharz, Wojciech - 200567 pl
dc.contributor.authorKurdyka, Krzysztofpl
dc.date.accessioned2023-02-20T13:55:40Z
dc.date.available2023-02-20T13:55:40Z
dc.date.issued2023pl
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.number1pl
dc.description.versionostateczna wersja wydawcy
dc.description.volume29pl
dc.identifier.articleid16pl
dc.identifier.doi10.1007/s00029-022-00824-9pl
dc.identifier.eissn1420-9020pl
dc.identifier.issn1022-1824pl
dc.identifier.project2018/31/B/ST1/01059pl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/308032
dc.languageengpl
dc.language.containerengpl
dc.rightsUdzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa*
dc.rights.licenceCC-BY
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/legalcode.pl*
dc.share.typeinne
dc.subject.enreal analytic functionpl
dc.subject.enarc-analytic functionpl
dc.subject.ensubanalytic functionpl
dc.subject.enNash functionpl
dc.subject.enarc-Nash functionpl
dc.subtypeArticlepl
dc.titleAnalytic functions and Nash functions along curvespl
dc.title.journalSelecta Mathematica. New Seriespl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
Let $X$ be a real analytic manifold. A function $f$ : $X \rightarrow \mathbb{R}$ is said to be curve-analytic if it is real analytic when restricted to any locally irreducible real analytic curve in $X$. We prove that every curve-analytic function with subanalytic graph is actually real analytic. To accomplish this task, we give a criterion for an arc-analytic function to be real analytic. A function is called arc-analytic if it is real analytic along any parametric real analytic arc. We also obtain analogous results for Nash manifolds and Nash functions, in which case the assumption of subanalyticity is superfluous.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.authorpl
Kucharz, Wojciech - 200567
dc.contributor.authorpl
Kurdyka, Krzysztof
dc.date.accessioned
2023-02-20T13:55:40Z
dc.date.available
2023-02-20T13:55:40Z
dc.date.issuedpl
2023
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.numberpl
1
dc.description.version
ostateczna wersja wydawcy
dc.description.volumepl
29
dc.identifier.articleidpl
16
dc.identifier.doipl
10.1007/s00029-022-00824-9
dc.identifier.eissnpl
1420-9020
dc.identifier.issnpl
1022-1824
dc.identifier.projectpl
2018/31/B/ST1/01059
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/308032
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
dc.rights.licence
CC-BY
dc.rights.uri*
http://creativecommons.org/licenses/by/4.0/legalcode.pl
dc.share.type
inne
dc.subject.enpl
real analytic function
dc.subject.enpl
arc-analytic function
dc.subject.enpl
subanalytic function
dc.subject.enpl
Nash function
dc.subject.enpl
arc-Nash function
dc.subtypepl
Article
dc.titlepl
Analytic functions and Nash functions along curves
dc.title.journalpl
Selecta Mathematica. New Series
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations

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