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VIDEO LIBRARY |
International Conference on Complex Analysis Dedicated to the memory of Andrei Gonchar and Anatoliy Vitushkin
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A general property of ideals in uniform algebras S. V. Kislyakovab a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences b St. Petersburg State University, Mathematics and Mechanics Faculty |
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Abstract: Let The question arose during the joint work of the author and I. Zlotnikov on interpolation properties of coinvariant subspaces of the shift operator. The answer indicated above may be viewed as a far-reaching generalization of the fact that $$ C_A= \{f\in C(\mathbb{T})\colon \hat{f}(n)=0\quad \text{for}\quad n<0\}. $$ The proof is based on the presence of certain very slight traces of analytic structure on an arbitrary proper uniform algebra. A similar technique was used by the author around 1987 for the proof of the Glicksberg conjecture. Language: english |