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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.
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Fields Institute Monographs
2009; 203 pp; hardcover
Volume: 25
ISBN-10: 0-8218-4734-1
ISBN-13: 978-0-8218-4734-3
List Price: US$65
Member Price: US$52
Order Code: FIM/25
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See also:

Bergman Spaces - Peter Duren and Alexander Schuster

Lectures on the Orbit Method - A A Kirillov

Operator Theory and Arithmetic in \(H^\infty\) - Hari Bercovici

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 co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

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

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