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Derivatives of Inner Functions

  • Book
  • © 2013

Overview

Authors:
  1. Javad Mashreghi

    1. , Département de mathématiques et de stati, Université Laval, Quebec, Canada

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  • Includes a comprehensive list of results on integral means taken from several research papers
  • Text is concise and self-contained, making it easily accessible to graduate students
  • Provides rapid access to the frontiers of research in this field

Part of the book series: Fields Institute Monographs (FIM, volume 31)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Inner Functions

    • Javad Mashreghi
    Pages 1-26

  3. The Exceptional Set of an Inner Function

    • Javad Mashreghi
    Pages 27-38

  4. The Derivative of Finite Blaschke Products

    • Javad Mashreghi
    Pages 39-50

  5. Angular Derivative

    • Javad Mashreghi
    Pages 51-70

  6. H p-Means of S′

    • Javad Mashreghi
    Pages 71-81

  7. B p-Means of S′

    • Javad Mashreghi
    Pages 83-97

  8. The Derivative of a Blaschke Product

    • Javad Mashreghi
    Pages 99-124

  9. H p-Means of B′

    • Javad Mashreghi
    Pages 125-143

  10. B p-Means of B′

    • Javad Mashreghi
    Pages 145-155

  11. The Growth of Integral Means of B′

    • Javad Mashreghi
    Pages 157-166

  12. Back Matter

    Pages 167-169
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Keywords

About this book

​Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal problems of complex analysis. They have been extensively studied since early last century, and the literature on this topic is vast. Therefore, this book is devoted to a concise study of derivatives of these objects, and confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means. The goal is to provide rapid access to the frontiers of research in this field. This monograph will allow researchers to get acquainted with essentials on inner functions, and it is self-contained, which makes it accessible to graduate students.

Reviews

From the reviews:

“This short monograph presents an account with full proofs of early investigations from around 1970–1980 on derivatives of inner functions … . the author also revisits Carathéodory’s theory on angular derivatives and gives a brief glimpse on Frostman’s results on exceptional sets for inner functions. … It fits well for student seminars.” (Raymond Mortini, Mathematical Reviews, August, 2013)

Authors and Affiliations

  • , Département de mathématiques et de stati, Université Laval, Quebec, Canada

    Javad Mashreghi

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