Beurling-Malliavin theory for Toeplitz kernels

• 成果类型: Article
• 署名作者: Makarov, N.; Poltoratski, A.
• 署名单位: Texas A&M University System; Texas A&M University College Station; California Institute of Technology
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0234-2
• 发表日期: 2010
• 页码: 443-480
• 关键词: spaces

摘要

We consider the family of Toeplitz operators T-J (S) over bara acting in the Hardy space H-2 in the upper halfplane; J and S are given meromorphic inner functions, and a is a real parameter. In the case where the argument of S has a power law type behavior on the real line, we compute the critical value c(J, S) = inf {a : ker T-J (S) over bara not equal 0}. The formula for c(J, S) generalizes the Beurling-Malliavin theorem on the radius of completeness for a system of exponentials.