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Bergman Spaces

Peter Duren University of Michigan, Ann Arbor, MI
Alexander Schuster San Francisco State University, San Francisco, CA
Available Formats:
Hardcover ISBN: 978-0-8218-0810-8
Product Code: SURV/100
List Price: $98.00 MAA Member Price:$88.20
AMS Member Price: $78.40 Electronic ISBN: 978-1-4704-1327-9 Product Code: SURV/100.E List Price:$92.00
MAA Member Price: $82.80 AMS Member Price:$73.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $147.00 MAA Member Price:$132.30
AMS Member Price: $117.60 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 Available Formats:  Hardcover ISBN: 978-0-8218-0810-8 Product Code: SURV/100  List Price:$98.00 MAA Member Price: $88.20 AMS Member Price:$78.40
 Electronic ISBN: 978-1-4704-1327-9 Product Code: SURV/100.E
 List Price: $92.00 MAA Member Price:$82.80 AMS Member Price: $73.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$147.00 MAA Member Price: $132.30 AMS Member Price:$117.60
• 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.

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

• Requests

Review Copy – for reviewers who would like to review an AMS book
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.

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 reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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