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Analytic Functions Smooth up to the Boundary

  • Book
  • © 1988

Overview

Authors:
  1. Nikolai A. Shirokov
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    You can also search for this author in PubMed   Google Scholar

Editors:
  1. Sergei V. Khrushchev
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    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-III
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  2. Introduction

    • Nikolai A. Shirokov
    Pages 1-19

  3. Notations

    • Nikolai A. Shirokov
    Pages 21-24

  4. The (F)-property

    • Nikolai A. Shirokov
    Pages 25-53

  5. Moduli of analytic functions smooth up to the boundary

    • Nikolai A. Shirokov
    Pages 54-135

  6. Zeros and their multiplicities

    • Nikolai A. Shirokov
    Pages 136-173

  7. Closed ideals in the space X pq μ (ω,ℓ)

    • Nikolai A. Shirokov
    Pages 174-205

  8. Back Matter

    Pages 207-212
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Keywords

About this book

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function, the generalization of the theorem of V.P. Havin and F.A. Shamoyan also known in the mathematical lore as the unpublished Carleson-Jacobs theorem, the complete description of the zero-set of analytic functions continuous up to the boundary, generalizing the classical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

Bibliographic Information

  • Book Title: Analytic Functions Smooth up to the Boundary

  • Authors: Nikolai A. Shirokov

  • Editors: Sergei V. Khrushchev

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0082810

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-19255-8Published: 11 May 1988

  • eBook ISBN: 978-3-540-39175-3Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: CCXXVIII, 222

  • Topics: Analysis

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