Physical Sciences and Mathematics Commons^™

An Extremal Problem For Characteristic Functions, Stephan Ramon Garcia, Isabelle Chalendar, Williams T. Ross, Dan Timotin

Pomona Faculty Publications and Research

Suppose E is a subset of the unit circle T and H^infinity C L^infinity is the Hardy subalgebra. We examine the problem of finding the distance from the characteristic function of E to zⁿH^infinity. This admits an alternate description as a dual extremal problem. Precise solutions are given in several important cases. The techniques used involve the theory of Toeplitz and Hankel operators as well as the construction of certain conformal mappings.