- Series
- Dissertation Defense
- Time
- Friday, April 16, 2021 - 4:00pm for 1.5 hours (actually 80 minutes)
- Location
- ONLINE
- Speaker
- Yam-Sung Cheng – Georgia Institute of Technology – ycheng61@gatech.edu
- Organizer
- Yam Sung Cheng
The main topics of this thesis concern two types of approximate Schauder frames for the Banach sequence space ℓ1. The first main topic pertains to finite-unit norm tight frames (FUNTFs) for the finite-dimensional real sequence space ℓn1. We prove that for any N≥n, FUNTFs of length N exist for real ℓn1. To show the existence of FUNTFs, 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 ℓn1 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 ℓ1. 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 ℓ1-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 ℓ1-type of frame inequality.
Bluejeans link to meeting: https://bluejeans.com/544995272