Reproducing kernel Hailbert space associated with a unitary representation of a groupoid

2021
journal article
article
dc.abstract.enThe aim of the paper is to create a link between the theory of reproducing kernel Hilbert spaces (RKHS) and the notion of a unitary representation of a group or of a groupoid. More specifically, it is demonstrated on one hand how to construct a positive definite kernel and anRKHSfor a given unitary representation of a group(oid), and on the other hand how to retrieve the unitary representation of a group or a groupoid from a positive definite kernel defined on that group(oid) with the help of the Moore-Aronszajn theorem. The kernel constructed from the group(oid) representation is inspired by the kernel defined in terms of the convolution of functions on a locally compact group. Several illustrative examples of reproducing kernels related with unitary representations of groupoids are discussed in detail. The paper is concluded with the brief overview of the possible applications of the proposed constructions.pl
dc.affiliationPion Prorektora ds. współpracy międzynarodowej : Centrum Kopernika Badań Interdyscyplinarnychpl
dc.contributor.authorDrewnik, Monikapl
dc.contributor.authorMiller, Tomasz - 410326 pl
dc.contributor.authorPasternak-Winiarski, Zbigniewpl
dc.date.accessioned2022-09-26T07:48:35Z
dc.date.available2022-09-26T07:48:35Z
dc.date.issued2021pl
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.number5pl
dc.description.versionostateczna wersja wydawcy
dc.description.volume15pl
dc.identifier.articleid91pl
dc.identifier.doi10.1007/s11785-021-01137-zpl
dc.identifier.eissn1661-8262pl
dc.identifier.issn1661-8254pl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/300124
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.enreproducing kernel Hilbert spacespl
dc.subject.enunitary representationpl
dc.subject.engroupoidpl
dc.subject.engrouppl
dc.subject.enhaar measurepl
dc.subject.enconvolutionpl
dc.subtypeArticlepl
dc.titleReproducing kernel Hailbert space associated with a unitary representation of a groupoidpl
dc.title.journalComplex Analysis and Operator Theorypl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
The aim of the paper is to create a link between the theory of reproducing kernel Hilbert spaces (RKHS) and the notion of a unitary representation of a group or of a groupoid. More specifically, it is demonstrated on one hand how to construct a positive definite kernel and anRKHSfor a given unitary representation of a group(oid), and on the other hand how to retrieve the unitary representation of a group or a groupoid from a positive definite kernel defined on that group(oid) with the help of the Moore-Aronszajn theorem. The kernel constructed from the group(oid) representation is inspired by the kernel defined in terms of the convolution of functions on a locally compact group. Several illustrative examples of reproducing kernels related with unitary representations of groupoids are discussed in detail. The paper is concluded with the brief overview of the possible applications of the proposed constructions.
dc.affiliationpl
Pion Prorektora ds. współpracy międzynarodowej : Centrum Kopernika Badań Interdyscyplinarnych
dc.contributor.authorpl
Drewnik, Monika
dc.contributor.authorpl
Miller, Tomasz - 410326
dc.contributor.authorpl
Pasternak-Winiarski, Zbigniew
dc.date.accessioned
2022-09-26T07:48:35Z
dc.date.available
2022-09-26T07:48:35Z
dc.date.issuedpl
2021
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.numberpl
5
dc.description.version
ostateczna wersja wydawcy
dc.description.volumepl
15
dc.identifier.articleidpl
91
dc.identifier.doipl
10.1007/s11785-021-01137-z
dc.identifier.eissnpl
1661-8262
dc.identifier.issnpl
1661-8254
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/300124
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
reproducing kernel Hilbert spaces
dc.subject.enpl
unitary representation
dc.subject.enpl
groupoid
dc.subject.enpl
group
dc.subject.enpl
haar measure
dc.subject.enpl
convolution
dc.subtypepl
Article
dc.titlepl
Reproducing kernel Hailbert space associated with a unitary representation of a groupoid
dc.title.journalpl
Complex Analysis and Operator Theory
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations

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