Banach Algebras of Integral Operators, Off-Diagonal Decay, and Applications in Wireless Communications
Abstract
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.
Keywords
Cite
@article{arxiv.math/0406198,
title = {Banach Algebras of Integral Operators, Off-Diagonal Decay, and Applications in Wireless Communications},
author = {Scott Beaver},
journal= {arXiv preprint arXiv:math/0406198},
year = {2007}
}
Comments
116 pages, 20 figures, dissertation