Analytic Functions Smooth up to the Boundary

Nikolai A. Shirokov (auth.), Sergei V. Khrushchev (eds.)3540192557, 9783540192558

This research monograph concerns the Nevanlinna factorization of analytic functions smooth, in a sense, up to the boundary. The peculiar properties of such a factorization are investigated for the most common classes of Lipschitz-like analytic functions. The book sets out to create a satisfactory factorization theory as exists for Hardy classes. The reader will find, among other things, the theorem on smoothness for the outer part of a function, the generalization of the theorem of V.P. Havin and F.A. Shamoyan also known in the mathematical lore as the unpublished Carleson-Jacobs theorem, the complete description of the zero-set of analytic functions continuous up to the boundary, generalizing the classical Carleson-Beurling theorem, and the structure of closed ideals in the new wide range of Banach algebras of analytic functions. The first three chapters assume the reader has taken a standard course on one complex variable; the fourth chapter requires supplementary papers cited there. The monograph addresses both final year students and doctoral students beginning to work in this area, and researchers who will find here new results, proofs and methods.

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Table of contents :
Introduction….Pages 1-19
Notations….Pages 21-24
The (F)-property….Pages 25-53
Moduli of analytic functions smooth up to the boundary….Pages 54-135
Zeros and their multiplicities….Pages 136-173
Closed ideals in the space X pq μ (ω,ℓ)….Pages 174-205