Spectral triples and wavelets for higher-rank graphs
DC Field | Value | Language |
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dc.contributor.author | Farsi, Carla | - |
dc.contributor.author | Gillaspy, Elizabeth | - |
dc.contributor.author | Julien, Antoine | - |
dc.contributor.author | Kang, Sooran | - |
dc.contributor.author | Packer, Judith | - |
dc.date.available | 2020-04-10T02:21:48Z | - |
dc.date.issued | 2020-02-15 | - |
dc.identifier.issn | 0022-247X | - |
dc.identifier.issn | 1096-0813 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/38181 | - |
dc.description.abstract | In this paper, we present a new way to associate a finitely summable spectral triple to a higher-rank graph Λ, via the infinite path space Λ∞ of Λ. Moreover, we prove that this spectral triple has a close connection to the wavelet decomposition of Λ∞ which was introduced by Farsi, Gillaspy, Kang, and Packer in 2015. We first introduce the concept of stationary k-Bratteli diagrams, in order to associate a family of ultrametric Cantor sets, and their associated Pearson-Bellissard spectral triples, to a finite, strongly connected higher-rank graph Λ. We then study the zeta function, abscissa of convergence, and Dixmier trace associated to the Pearson-Bellissard spectral triples of these Cantor sets, and show these spectral triples are ζ-regular in the sense of Pearson and Bellissard. We obtain an integral formula for the Dixmier trace given by integration against a measure μ, and show that μ is a rescaled version of the measure M on Λ∞ which was introduced by an Huef, Laca, Raeburn, and Sims. Finally, we investigate the eigenspaces of a family of Laplace-Beltrami operators associated to the Dirichlet forms of the spectral triples. We show that these eigenspaces refine the wavelet decomposition of L2(Λ∞,M) which was constructed by Farsi et al. © 2019 | - |
dc.language | 영어 | - |
dc.language.iso | ENG | - |
dc.publisher | Academic Press Inc. | - |
dc.title | Spectral triples and wavelets for higher-rank graphs | - |
dc.type | Article | - |
dc.identifier.doi | 10.1016/j.jmaa.2019.123572 | - |
dc.identifier.bibliographicCitation | Journal of Mathematical Analysis and Applications, v.482, no.2 | - |
dc.description.isOpenAccess | N | - |
dc.identifier.wosid | 000495147200017 | - |
dc.identifier.scopusid | 2-s2.0-85072895757 | - |
dc.citation.number | 2 | - |
dc.citation.title | Journal of Mathematical Analysis and Applications | - |
dc.citation.volume | 482 | - |
dc.type.docType | Article | - |
dc.publisher.location | 미국 | - |
dc.subject.keywordAuthor | Dixmier trace | - |
dc.subject.keywordAuthor | Finitely summable spectral triple | - |
dc.subject.keywordAuthor | Higher-rank graph | - |
dc.subject.keywordAuthor | Laplace-Beltrami operator | - |
dc.subject.keywordAuthor | Wavelets | - |
dc.subject.keywordAuthor | ζ-function | - |
dc.subject.keywordPlus | C-ASTERISK-ALGEBRAS | - |
dc.subject.keywordPlus | KMS STATES | - |
dc.subject.keywordPlus | DIRAC OPERATORS | - |
dc.subject.keywordPlus | SINGULAR TRACES | - |
dc.subject.keywordPlus | SPACES | - |
dc.subject.keywordPlus | PERIODICITY | - |
dc.subject.keywordPlus | SIMPLICITY | - |
dc.subject.keywordPlus | GEOMETRY | - |
dc.subject.keywordPlus | SUMS | - |
dc.subject.keywordPlus | SETS | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
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