Article - preprint
Extremal problem, truncated Toeplitz operator, Toeplitz operator, Hankel operator, complex symmetric operator
Suppose E is a subset of the unit circle T and Hinfinity C Linfinity is the Hardy subalgebra. We examine the problem of finding the distance from the characteristic function of E to znHinfinity. 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.
© 2014 American Mathematical Society
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.