Circular spectrum of bounded functions and an application to difference equations,   Gaston M. N’Guérékata,   Morgan State University,  Mon, 12 November, 2012,   9:00 a.m. A-227


We introduce the new concept of circular spectrum of bounded functions and show its relation to the Carleman spectrum. Then we use this tool to prove the existence and uniqueness of almost periodic, compact al- most automorphic or almost automorphic solution of the difference equation u(t) = B(t)u(t -1) + f(t), where B(t) is a linear, strongly continuous, and 1-periodic operator in a Banach space X.