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Topics in Hardy Classes and Univalent Functions

  • Marvin Rosenblum
  • James Rovnyak

Part of the Birkhäuser Advanced Texts book series (BAT)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Marvin Rosenblum, James Rovnyak
    Pages 1-22
  3. Marvin Rosenblum, James Rovnyak
    Pages 23-33
  4. Marvin Rosenblum, James Rovnyak
    Pages 55-80
  5. Marvin Rosenblum, James Rovnyak
    Pages 81-115
  6. Marvin Rosenblum, James Rovnyak
    Pages 117-136
  7. Marvin Rosenblum, James Rovnyak
    Pages 137-180
  8. Marvin Rosenblum, James Rovnyak
    Pages 181-207
  9. Marvin Rosenblum, James Rovnyak
    Pages 209-231
  10. Back Matter
    Pages 233-251

About this book

Introduction

These notes are based on lectures given at the University of Virginia over the past twenty years. They may be viewed as a course in function theory for nonspecialists. Chapters 1-6 give the function-theoretic background to Hardy Classes and Operator Theory, Oxford Mathematical Monographs, Oxford University Press, New York, 1985. These chapters were written first, and they were origi­ nally intended to be a part of that book. Half-plane function theory continues to be useful for applications and is a focal point in our account (Chapters 5 and 6). The theory of Hardy and Nevanlinna classes is derived from proper­ ties of harmonic majorants of subharmonic functions (Chapters 3 and 4). A selfcontained treatment of harmonic and subharmonic functions is included (Chapters 1 and 2). Chapters 7-9 present concepts from the theory of univalent functions and Loewner families leading to proofs of the Bieberbach, Robertson, and Milin conjectures. Their purpose is to make the work of de Branges accessible to students of operator theory. These chapters are by the second author. There is a high degree of independence in the chapters, allowing the material to be used in a variety of ways. For example, Chapters 5-6 can be studied alone by readers familiar with function theory on the unit disk. Chapters 7-9 have been used as the basis for a one-semester topics course.

Keywords

Algebra Blaschke product Complex analysis Finite Morphism Nevanlinna theory Operator theory Poisson kernel calculus equation function linear optimization proof theorem

Authors and affiliations

  • Marvin Rosenblum
    • 1
  • James Rovnyak
    • 1
  1. 1.Department of Mathematics Mathematics-Astronomy BuildingUniversity of VirginiaCharlottesvilleUSA

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