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Hardcover ISBN:  9780821847343 
Product Code:  FIM/25 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $62.40 
eBook ISBN:  9781470417888 
Product Code:  FIM/25.E 
List Price:  $73.00 
MAA Member Price:  $65.70 
AMS Member Price:  $58.40 
Hardcover ISBN:  9780821847343 
eBook ISBN:  9781470417888 
Product Code:  FIM/25.B 
List Price:  $151.00 $114.50 
MAA Member Price:  $135.90 $103.05 
AMS Member Price:  $120.80 $91.60 

Book DetailsFields Institute MonographsVolume: 25; 2009; 203 ppMSC: 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.
Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipGraduate students and research mathematicians interested in function theory in the unit disk and ball, and interpoloation and corona problems.

Table of Contents

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 NevanlinnaPick kernels

Chapter 6. Carleson measures for the HardySobolev 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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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.
Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
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 NevanlinnaPick kernels

Chapter 6. Carleson measures for the HardySobolev 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