Birkhäuser Advanced Texts Basler Lehrbücher

Topics in Hardy Classes and Univalent Functions

Authors: Rosenblum, Marvin, Rovnyak, James

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About this Textbook

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.

Table of contents (9 chapters)

  • Harmonic Functions

    Rosenblum, Marvin (et al.)

    Pages 1-22

  • Subharmonic Functions

    Rosenblum, Marvin (et al.)

    Pages 23-33

  • Part I. Harmonic Majorants Part II. Nevanlinna and Hardy-Orlicz Classes

    Rosenblum, Marvin (et al.)

    Pages 35-53

  • Hardy Spaces on the Disk

    Rosenblum, Marvin (et al.)

    Pages 55-80

  • Function Theory on a Half-Plane

    Rosenblum, Marvin (et al.)

    Pages 81-115

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-0348-8520-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-3-7643-5111-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-3-0348-9662-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topics in Hardy Classes and Univalent Functions
Authors
Series Title
Birkhäuser Advanced Texts Basler Lehrbücher
Copyright
1994
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8520-1
DOI
10.1007/978-3-0348-8520-1
Hardcover ISBN
978-3-7643-5111-3
Softcover ISBN
978-3-0348-9662-7
Series ISSN
1019-6242
Edition Number
1
Number of Pages
XII, 250
Topics