dc.contributor.author Charina, Maria dc.contributor.author Putinar, Mihai dc.contributor.author Scheiderer, Claus dc.contributor.author Stöckler, Joachim dc.date.accessioned 2012-08-13T12:00:00Z dc.date.accessioned 2016-10-05T14:14:24Z dc.date.available 2012-08-13T12:00:00Z dc.date.available 2016-10-05T14:14:24Z dc.date.issued 2012-08-13 dc.identifier.uri http://publications.mfo.de/handle/mfo/1214 dc.description Research in Pairs 2011 en_US dc.description.abstract Recent 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.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2012,11 dc.subject Multivariate wavelet frame en_US dc.subject Real algebraic geometry en_US dc.subject Torus en_US dc.subject Hermitian square en_US dc.subject Polynomial optimization en_US dc.subject Trigonometric polynomial en_US dc.title A real algebra perspective on multivariate tight wavelet frames en_US dc.type Preprint en_US dc.rights.license Dieses 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.license This 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.doi 10.14760/OWP-2012-11 local.scientificprogram Research in Pairs 2011 local.series.id OWP-2012-11 local.subject.msc 65 local.subject.msc 12 local.subject.msc 90 dc.identifier.urn urn:nbn:de:101:1-2012081013886 dc.identifier.ppn 1651666377
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