Suppose E is a subset of the unit circle T and H∞C L∞ is the Hardy subalgebra. We examine the problem of Finding the distance from the characteristic function of E to zn H∞. 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.
Copyright © 2013 arXiv.
The definitive version is available at: http://arxiv.org/abs/1307.2646
Ross, William T., Isabelle Chalendar, Stephan Ramon Garcia, and Dan Timotin. "An Extremal Problem for Characteristic Functions." ArXiv, 2013, 1-23.
Ross, William T.; Chalendar, Isabelle; Garcia, Stephan Ramon; and Timotin, Dan, "An Extremal Problem for Characteristic Functions" (2013). Math and Computer Science Faculty Publications. 121.