Analytic Functions Smooth up to the Boundary

Nikolai A. Shirokov

ISBN 10: 3540192557 / ISBN 13: 9783540192558

Editore: Springer Berlin Heidelberg Mai 1988, 1988

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This item is printed on demand - it takes 3-4 days longer - Neuware -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function, the generalization of the theorem of V.P. Havin and F.A. Shamoyan also known in the mathematical lore as the unpublished Carleson-Jacobs theorem, the complete description of the zero-set of analytic functions continuous up to the boundary, generalizing the classical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. 228 pp. Englisch. Codice articolo 9783540192558

Dati bibliografici

Titolo: Analytic Functions Smooth up to the Boundary

Casa editrice: Springer Berlin Heidelberg Mai 1988

Data di pubblicazione: 1988

Legatura: Taschenbuch

Condizione: Neu

Descrizione articolo

Riassunto:

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function, the generalization of the theorem of V.P. Havin and F.A. Shamoyan also known in the mathematical lore as the unpublished Carleson-Jacobs theorem, the complete description of the zero-set of analytic functions continuous up to the boundary, generalizing the classical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.

Contenuti:

Notations.- The (F)-property.- Moduli of analytic functions smooth up to the boundary.- Zeros and their multiplicities.- Closed ideals in the space X pq ? (?,?).