2004/06/09 by Scott Beaver, Beaver, Scott
Computer Science · Engineering · Mathematics · #47L80 #Digital Filter Design and Implementation #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Ultra-Wideband Communications Technology #math.FA #math.OA #msc:47L80
paper · pdf · doi:10.48550/arxiv.math/0406198
116 pages, 20 figures, dissertation
arxiv created 2004/06/09 · openalex publication_date 2004/06/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this dissertation I establish that a broad class of Banach *-algebras of infinite integral operators, defined by the property that the kernels of the elements of the algebras possess subexponential off-diagonal decay, is inverse closed in the Banach space of bounded linear operators on the Hilbert space of square-integrable functions. I also show that the algebras under consideration are symmetric. In the second part of this dissertation, I present the results of the IEEE Transactions on Communications paper written jointly by Thomas Strohmer and me. We develop a comprehensive framework for the design of orthogonal frequency-division multiplexing (OFDM) systems, using techniques from Gabor frame theory, sphere-packing theory, representation theory, and the Heisenberg group.