Existence and construction of real-valued equiangular tight frames

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Existence and construction of real-valued equiangular tight frames

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/6854

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dc.contributor.advisor Casazza, Peter G., 1945- en_US
dc.contributor.author Redmond, Daniel Joseph en_US
dc.date.accessioned 2010-04-19T14:36:12Z
dc.date.available 2010-04-19T14:36:12Z
dc.date.issued 2009 en_US
dc.date.submitted 2009 Fall en_US
dc.identifier.other RedmondD-121109-D926 en_US
dc.identifier.uri http://hdl.handle.net/10355/6854
dc.description Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 24, 2010). en_US
dc.description The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. en_US
dc.description Dissertation advisor: Dr. Peter Casazza. en_US
dc.description Vita. en_US
dc.description Includes bibliographical references. en_US
dc.description Ph. D. University of Missouri--Columbia 2009. en_US
dc.description Dissertations, Academic -- University of Missouri--Columbia -- Mathematics. en_US
dc.description.abstract This paper presents results on real-valued equiangular tight frames (ETFs) and related topics. Some geometric theorems are developed, and aspects of frame theory are used to gain insight into ETFs. We develop a projection method for analyzing equiangular tight frames that leads to new existence results, and that establishes a link between the geometry of the ETF and the spectrum of the associated Gramian and signature matrices. A new lower bound on the number of frame vectors improves on the best known necessary conditions for existence. We recover the Holmes-Paulsen criterion two different ways, along with additional necessary conditions. We also show that ETFs can be rotated to match a standard position, and that this corresponds to a binary tree structure (partial ordering) of embedded sub-spheres of decreasing dimension. This leads to a new canonical form and an enumerative algorithm to algebraically construct or prove the non-existence of equiangular tight frames. en_US
dc.format.extent ix, 99 pages en_US
dc.language.iso en_US en_US
dc.publisher University of Missouri--Columbia en_US
dc.relation.ispartof 2009 Freely available dissertations (MU) en_US
dc.subject Equiangular tight frames en_US
dc.subject.lcsh Frames (Combinatorial analysis) en_US
dc.title Existence and construction of real-valued equiangular tight frames en_US
dc.type Thesis en_US
thesis.degree.discipline Mathematics en_US
thesis.degree.grantor University of Missouri--Columbia en_US
thesis.degree.name Ph. D. en_US
thesis.degree.level Doctoral en_US
dc.identifier.oclc 605910420 en_US
dc.relation.ispartofcommunity University of Missouri-Columbia. Graduate School. Theses and Dissertations. Dissertations. 2009 Dissertations


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