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dc.contributor.advisorHeil, Christopher
dc.contributor.authorCheng, Yam-Sung
dc.date.accessioned2021-06-10T16:55:52Z
dc.date.available2021-06-10T16:55:52Z
dc.date.created2021-05
dc.date.issued2021-04-29
dc.date.submittedMay 2021
dc.identifier.urihttp://hdl.handle.net/1853/64763
dc.description.abstractThe main topics of this thesis concern two types of approximate Schauder frames for the Banach sequence space l_1^n. The first main topic pertains to finite-unit norm tight frames (FUNTFs) for the finite-dimensional real sequence space l_1^n. We prove the existence of FUNTFs for real l_1^n. To do so, specific examples are constructed for various lengths. These constructions involve repetitions of frame elements. However, a different method of frame constructions allows us to prove the existence of FUNTFs for real l_1^n of lengths 2n−1 and 2n−2 that do not have repeated elements. The second main topic of this thesis pertains to normalized unconditional Schauder frames for the sequence space l_1. A Schauder frame provides a reconstruction formula for elements in the space, but need not be associated with a frame inequality. Our main theorem on this topic establishes a set of conditions under which an l_1-type of frame inequality is applicable towards unconditional Schauder frames. A primary motivation for choosing this set of hypotheses involves appropriate modifications of the Rademacher system, a version of which we prove to be an unconditional Schauder frame that does not satisfy an l_1-type of frame inequality.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectMathematics
dc.subjectHarmonic analysis
dc.subjectFrame theory
dc.subjectBanach spaces
dc.titleApproximate Schauder Frames for Banach Sequence Spaces
dc.typeDissertation
dc.description.degreePh.D.
dc.contributor.departmentMathematics
thesis.degree.levelDoctoral
dc.contributor.committeeMemberFreeman, Daniel
dc.contributor.committeeMemberLi, Wing
dc.contributor.committeeMemberPowell, Alexander
dc.contributor.committeeMemberNitzan, Shahaf
dc.date.updated2021-06-10T16:55:52Z


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