An Extremal Problem for Characteristic Functions

Authors

Stephan Ramon Garcia, Pomona CollegeFollow
Isabelle Chalendar, University of Lyon
Williams T. Ross, University of Richmond
Dan Timotin, Simion Stoilow Institute of Mathematics of the Romanian Academy

Document Type

Article - preprint

Department

Mathematics (Pomona)

Publication Date

2014

Keywords

Extremal problem, truncated Toeplitz operator, Toeplitz operator, Hankel operator, complex symmetric operator

Abstract

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.

Comments

Pre-print from https://arxiv.org/pdf/1307.2646v2.pdf

Final publication can be found at:

Chalendar, I., Garcia, S.R., Ross, W.T., Timotin, D., An extremal problem for characteristic functions, Trans. Amer. Math. Soc. 368 (2014), no. 6, 4115-4135.

Rights Information

© 2014 American Mathematical Society

Recommended Citation

Chalendar, I., Garcia, S.R., Ross, W.T., Timotin, D. "An Extremal Problem for Characteristic Functions," Transactions of the American Mathematical Society 368 (2014), no. 6, 4115-4135.