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dc.contributor.advisorCasazza, Peter G., 1945-eng
dc.contributor.authorRedmond, Daniel Josepheng
dc.date.issued2009eng
dc.date.submitted2009 Falleng
dc.descriptionTitle from PDF of title page (University of Missouri--Columbia, viewed on Feb 24, 2010).eng
dc.descriptionThe 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.eng
dc.descriptionDissertation advisor: Dr. Peter Casazza.eng
dc.descriptionVita.eng
dc.descriptionIncludes bibliographical references.eng
dc.descriptionPh. D. University of Missouri--Columbia 2009.eng
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Mathematics.eng
dc.description.abstractThis 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.eng
dc.format.extentix, 99 pageseng
dc.identifier.oclc605910420eng
dc.identifier.otherRedmondD-121109-D926eng
dc.identifier.urihttp://hdl.handle.net/10355/6854eng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartof2009 Freely available dissertations (MU)eng
dc.relation.ispartofcommunityUniversity of Missouri-Columbia. Graduate School. Theses and Dissertations. Dissertations. 2009 Dissertationseng
dc.subjectEquiangular tight frameseng
dc.subject.lcshFrames (Combinatorial analysis)eng
dc.titleExistence and construction of real-valued equiangular tight frameseng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


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