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Bergman Spaces
 
Peter Duren University of Michigan, Ann Arbor, MI
Alexander Schuster San Francisco State University, San Francisco, CA
Bergman Spaces
Softcover ISBN:  978-0-8218-4315-4
Product Code:  SURV/100.S
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Not yet published - Preorder Now!
Expected availability date: May 15, 2024
eBook ISBN:  978-1-4704-1327-9
Product Code:  SURV/100.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4315-4
eBook: ISBN:  978-1-4704-1327-9
Product Code:  SURV/100.S.B
List Price: $250.00 $187.50
MAA Member Price: $225.00 $168.75
AMS Member Price: $200.00 $150.00
Not yet published - Preorder Now!
Expected availability date: May 15, 2024
Bergman Spaces
Click above image for expanded view
Bergman Spaces
Peter Duren University of Michigan, Ann Arbor, MI
Alexander Schuster San Francisco State University, San Francisco, CA
Softcover ISBN:  978-0-8218-4315-4
Product Code:  SURV/100.S
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Not yet published - Preorder Now!
Expected availability date: May 15, 2024
eBook ISBN:  978-1-4704-1327-9
Product Code:  SURV/100.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4315-4
eBook ISBN:  978-1-4704-1327-9
Product Code:  SURV/100.S.B
List Price: $250.00 $187.50
MAA Member Price: $225.00 $168.75
AMS Member Price: $200.00 $150.00
Not yet published - Preorder Now!
Expected availability date: May 15, 2024
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1002004; 318 pp
    MSC: Primary 30; 46

    Over the last ten years, the theory of Bergman spaces has undergone a remarkable metamorphosis. In a series of major advances, central problems once considered intractable were solved, and a rich theory emerged. Although progress continues, the time seems ripe for a full and unified account of the subject, weaving the old and new results together. This thorough exposition provides just that.

    The subject of Bergman spaces is a masterful blend of complex function theory with functional analysis and operator theory. It has much in common with Hardy spaces, but involves new elements such as hyperbolic geometry, reproducing kernels, and biharmonic Green functions.

    In this book, the authors develop background material and provide a self-contained introduction to a broad range of topics, including recent advances on interpolation and sampling, contractive zero-divisors, and invariant subspaces. The book is accessible to researchers and advanced graduate students who have studied basic complex function theory, measure theory, and functional analysis.

    Readership

    Advanced graduate students and research mathematicians interested in complex function theory and operator theory.

  • Table of Contents
     
     
    • Chapters
    • 0. Overview
    • 1. The Bergman kernel function
    • 2. Linear space properties
    • 3. Analytic properties
    • 4. Zero-sets
    • 5. Contractive zero-divisors
    • 6. Sampling and interpolation
    • 7. Proofs of sampling and interpolation theorems
    • 8. Invariant subspaces
    • 9. Structure of invariant subspaces
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1002004; 318 pp
MSC: Primary 30; 46

Over the last ten years, the theory of Bergman spaces has undergone a remarkable metamorphosis. In a series of major advances, central problems once considered intractable were solved, and a rich theory emerged. Although progress continues, the time seems ripe for a full and unified account of the subject, weaving the old and new results together. This thorough exposition provides just that.

The subject of Bergman spaces is a masterful blend of complex function theory with functional analysis and operator theory. It has much in common with Hardy spaces, but involves new elements such as hyperbolic geometry, reproducing kernels, and biharmonic Green functions.

In this book, the authors develop background material and provide a self-contained introduction to a broad range of topics, including recent advances on interpolation and sampling, contractive zero-divisors, and invariant subspaces. The book is accessible to researchers and advanced graduate students who have studied basic complex function theory, measure theory, and functional analysis.

Readership

Advanced graduate students and research mathematicians interested in complex function theory and operator theory.

  • Chapters
  • 0. Overview
  • 1. The Bergman kernel function
  • 2. Linear space properties
  • 3. Analytic properties
  • 4. Zero-sets
  • 5. Contractive zero-divisors
  • 6. Sampling and interpolation
  • 7. Proofs of sampling and interpolation theorems
  • 8. Invariant subspaces
  • 9. Structure of invariant subspaces
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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