An Extremal Problem for Characteristic Functions

Authors

William T. Ross, University of RichmondFollow
Isabelle Chalendar
Stephan Ramon Garcia
Dan Timotin

Abstract

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.

Document Type

Post-print Article

Publication Date

2013

Publisher Statement

Copyright © 2013 arXiv.

The definitive version is available at: http://arxiv.org/abs/1307.2646

Full Citation:

Ross, William T., Isabelle Chalendar, Stephan Ramon Garcia, and Dan Timotin. "An Extremal Problem for Characteristic Functions." ArXiv, 2013, 1-23.

Recommended Citation

Ross, William T.; Chalendar, Isabelle; Garcia, Stephan Ramon; and Timotin, Dan, "An Extremal Problem for Characteristic Functions" (2013). Department of Math & Statistics Faculty Publications. 121.
https://scholarship.richmond.edu/mathcs-faculty-publications/121