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dc.contributor.authorCharina, Maria
dc.contributor.authorPutinar, Mihai
dc.contributor.authorScheiderer, Claus
dc.contributor.authorStöckler, Joachim
dc.date.accessioned2012-08-13T12:00:00Z
dc.date.accessioned2016-10-05T14:14:24Z
dc.date.available2012-08-13T12:00:00Z
dc.date.available2016-10-05T14:14:24Z
dc.date.issued2012-08-13
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1214
dc.descriptionResearch in Pairs 2011en_US
dc.description.abstractRecent results from real algebraic geometry and the theory of polynomial optimization are related in a new framework to the existence question of multivariate tight wavelet frames whose generators have at least one vanishing moment. Namely, several equivalent formulations of the so-called Unitary Extension Principle (UEP) from are interpreted in terms of hermitian sums of squares of certain nongenative trigonometric polynomials and in terms of semi-definite programming. The latter together with the results in answer affirmatively the long stading open question of the existence of such tight wavelet frames in dimesion $d = 2$; we also provide numerically efficient methods for checking their existence and actual construction in any dimension. We exhibit a class of counterexamples in dimension $d = 3$ showing that, in general, the UEP property is not sufficient for the existence of tight wavelet frames. On the other hand we provide stronger sufficient conditions for the existence of tight wavelet frames in dimension $d ≥ 3$ and illustrate our results by several examples.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2012,11
dc.subjectMultivariate wavelet frameen_US
dc.subjectReal algebraic geometryen_US
dc.subjectTorusen_US
dc.subjectHermitian squareen_US
dc.subjectPolynomial optimizationen_US
dc.subjectTrigonometric polynomialen_US
dc.titleA real algebra perspective on multivariate tight wavelet framesen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2012-11
local.scientificprogramResearch in Pairs 2011
local.series.idOWP-2012-11
local.subject.msc65
local.subject.msc12
local.subject.msc90
dc.identifier.urnurn:nbn:de:101:1-2012081013886
dc.identifier.ppn1651666377


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