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.