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Function Theory: Interpolation and Corona Problems

Eric T. Sawyer McMaster University, Hamilton, ON, Canada
A co-publication of the AMS and Fields Institute
Available Formats:
Hardcover ISBN: 978-0-8218-4734-3
Product Code: FIM/25
List Price: $74.00 MAA Member Price:$66.60
AMS Member Price: $59.20 Electronic ISBN: 978-1-4704-1788-8 Product Code: FIM/25.E List Price:$69.00
MAA Member Price: $62.10 AMS Member Price:$55.20
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List Price: $111.00 MAA Member Price:$99.90
AMS Member Price: $88.80 Click above image for expanded view Function Theory: Interpolation and Corona Problems Eric T. Sawyer McMaster University, Hamilton, ON, Canada A co-publication of the AMS and Fields Institute Available Formats:  Hardcover ISBN: 978-0-8218-4734-3 Product Code: FIM/25  List Price:$74.00 MAA Member Price: $66.60 AMS Member Price:$59.20
 Electronic ISBN: 978-1-4704-1788-8 Product Code: FIM/25.E
 List Price: $69.00 MAA Member Price:$62.10 AMS Member Price: $55.20 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:$111.00 MAA Member Price: $99.90 AMS Member Price:$88.80
• Book Details

Fields Institute Monographs
Volume: 252009; 203 pp
MSC: Primary 30; 32; Secondary 42; 46;

These lecture notes take the reader from Lennart Carleson's first deep results on interpolation and corona problems in the unit disk to modern analogues in the disk and ball. The emphasis is on introducing the diverse array of techniques needed to attack these problems rather than producing an encyclopedic summary of achievements. Techniques from classical analysis and operator theory include duality, Blaschke product constructions, purely Hilbert space arguments, bounded mean oscillation, best approximation, boundedness of the Beurling transform, estimates on solutions to the $\bar\partial$ equation, the Koszul complex, use of trees, the complete Pick property, and the Toeplitz corona theorem. An extensive appendix on background material in functional analysis and function theory on the disk is included for the reader's convenience.

Graduate students and research mathematicians interested in function theory in the unit disk and ball, and interpoloation and corona problems.

• Chapters
• Chapter 1. Preliminaries
• Chapter 2. The interpolation problem
• Chapter 3. The corona problem
• Chapter 4. Toeplitz and Hankel operators
• Chapter 5. Hilbert function spaces and Nevanlinna-Pick kernels
• Chapter 6. Carleson measures for the Hardy-Sobolev spaces
• Appendix A. Functional analysis
• Appendix B. Weak derivatives and Sobolev spaces
• Appendix C. Function theory on the disk
• Appendix D. Spectral theory for normal operators

• Request Review Copy
Volume: 252009; 203 pp
MSC: Primary 30; 32; Secondary 42; 46;

These lecture notes take the reader from Lennart Carleson's first deep results on interpolation and corona problems in the unit disk to modern analogues in the disk and ball. The emphasis is on introducing the diverse array of techniques needed to attack these problems rather than producing an encyclopedic summary of achievements. Techniques from classical analysis and operator theory include duality, Blaschke product constructions, purely Hilbert space arguments, bounded mean oscillation, best approximation, boundedness of the Beurling transform, estimates on solutions to the $\bar\partial$ equation, the Koszul complex, use of trees, the complete Pick property, and the Toeplitz corona theorem. An extensive appendix on background material in functional analysis and function theory on the disk is included for the reader's convenience.

Graduate students and research mathematicians interested in function theory in the unit disk and ball, and interpoloation and corona problems.

• Chapters
• Chapter 1. Preliminaries
• Chapter 2. The interpolation problem
• Chapter 3. The corona problem
• Chapter 4. Toeplitz and Hankel operators
• Chapter 5. Hilbert function spaces and Nevanlinna-Pick kernels
• Chapter 6. Carleson measures for the Hardy-Sobolev spaces
• Appendix A. Functional analysis
• Appendix B. Weak derivatives and Sobolev spaces
• Appendix C. Function theory on the disk
• Appendix D. Spectral theory for normal operators
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