Title: Function Theory: Interpolation and Corona Problems (Fields Institute Monographs, 25)
Publisher: American Mathematical Society
Publication Date: 2009
Language: English
ISBN 10: 0821847341
ISBN 13: 9780821847343
Binding: Hardcover
Condition: New

About this title

Synopsis

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.

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