
Preface  Preview Material  Table of Contents  Supplementary Material 
Fields Institute Monographs 2009; 203 pp; hardcover Volume: 25 ISBN10: 0821847341 ISBN13: 9780821847343 List Price: US$65 Member Price: US$52 Order Code: FIM/25 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 copublished 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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