AN EXTREMAL PROBLEM FOR CHARACTERISTIC FUNCTIONS

作者：Chalendar Isabelle^*; Garcia Stephan Ramon^*; Ross William T^*; Timotin Dan^*

来源：Transactions of the American Mathematical Society, 2016, 368(6): 4115-4135.

DOI：10.1090/tran/6446

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

Suppose E is a subset of the unit circle T and H-infinity subset of L-infinity is the Hardy subalgebra. We examine the problem of finding the distance from the characteristic function of E to Z(n)H(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.

• 出版日期2016-6