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Analytic Functions Smooth up to the Boundary

  • Authors
  • Nikolai A. Shirokov
  • Editors
  • Sergei V. Khrushchev

Part of the Lecture Notes in Mathematics book series (LNM, volume 1312)

Table of contents

  1. Front Matter
    Pages I-III
  2. Nikolai A. Shirokov
    Pages 1-19
  3. Nikolai A. Shirokov
    Pages 21-24
  4. Nikolai A. Shirokov
    Pages 25-53
  5. Nikolai A. Shirokov
    Pages 136-173
  6. Nikolai A. Shirokov
    Pages 174-205
  7. Back Matter
    Pages 207-212

About this book

Introduction

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function, the generalization of the theorem of V.P. Havin and F.A. Shamoyan also known in the mathematical lore as the unpublished Carleson-Jacobs theorem, the complete description of the zero-set of analytic functions continuous up to the boundary, generalizing the classical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

Keywords

Nevanlinna theory Smooth function analytic function

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0082810
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-19255-8
  • Online ISBN 978-3-540-39175-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site