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Article: Fourier bases and Fourier frames on self-affine measures

TitleFourier bases and Fourier frames on self-affine measures
Authors
Dutkay, Dorin ErvinLai, Chun KitWang, Yang
Issue Date2017
Citation
Trends in Mathematics, 2017, v. PartF3, p. 87-111 How to Cite?
DOI: http://dx.doi.org/10.1007/978-3-319-57805-7_5
AbstractThis paper gives a review of the recent progress in the study of Fourier bases and Fourier frames on self-affine measures. In particular, we emphasize the new matrix analysis approach for checking the completeness of a mutually orthogonal set. This method helps us settle down a long-standing conjecture that Hadamard triples generate self-affine spectral measures. It also gives us non-trivial examples of fractal measures with Fourier frames. Furthermore, a new avenue is open to investigate whether the Middle-Third-Cantor measure admits Fourier frames.
Persistent Identifierhttp://hdl.handle.net/10722/363263
ISSN
2297-0215
2020 SCImago Journal Rankings: 0.190

 

DC FieldValueLanguage
dc.contributor.authorDutkay, Dorin Ervin-
dc.contributor.authorLai, Chun Kit-
dc.contributor.authorWang, Yang-
dc.date.accessioned2025-10-10T07:45:38Z-
dc.date.available2025-10-10T07:45:38Z-
dc.date.issued2017-
dc.identifier.citationTrends in Mathematics, 2017, v. PartF3, p. 87-111-
dc.identifier.issn2297-0215-
dc.identifier.urihttp://hdl.handle.net/10722/363263-
dc.description.abstractThis paper gives a review of the recent progress in the study of Fourier bases and Fourier frames on self-affine measures. In particular, we emphasize the new matrix analysis approach for checking the completeness of a mutually orthogonal set. This method helps us settle down a long-standing conjecture that Hadamard triples generate self-affine spectral measures. It also gives us non-trivial examples of fractal measures with Fourier frames. Furthermore, a new avenue is open to investigate whether the Middle-Third-Cantor measure admits Fourier frames.-
dc.languageeng-
dc.relation.ispartofTrends in Mathematics-
dc.titleFourier bases and Fourier frames on self-affine measures-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/978-3-319-57805-7_5-
dc.identifier.scopuseid_2-s2.0-85028755108-
dc.identifier.volumePartF3-
dc.identifier.spage87-
dc.identifier.epage111-
dc.identifier.eissn2297-024X-

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