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    Approximate Schauder Frames for Banach Sequence Spaces

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    CHENG-DISSERTATION-2021.pdf (529.7Kb)
    Date
    2021-04-29
    Author
    Cheng, Yam-Sung
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    Abstract
    The 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.
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    http://hdl.handle.net/1853/64763
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    • Georgia Tech Theses and Dissertations [23877]
    • School of Mathematics Theses and Dissertations [440]

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