Analytic Functions Smooth up to the Boundary (Lecture Notes in Mathematics) by Nikolai Shirokov
English | June 13, 1988 | ISBN: 3540192557, 0387192557 | 213 Pages | DJVU | 1 MB
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function, the generalization of the theorem of V.P. Havin and F.A. Shamoyan also known in the mathematical lore as the unpublished Carleson-Jacobs theorem, the complete description of the zero-set of analytic functions continuous up to the boundary, generalizing the classical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.
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