Monotone Matrix Functions and Analytic Continuation: 207 (Grundlehren der mathematischen Wissenschaften, 207) - Softcover

Donoghue, W.F.Jr.

Softcover

ISBN 10: 3642657575 ISBN 13: 9783642657573

Publisher: Springer, 2011

Synopsis

A Pick function is a function that is analytic in the upper half-plane with positive imaginary part. In the first part of this book we try to give a readable account of this class of functions as well as one of the standard proofs of the spectral theorem based on properties of this class. In the remainder of the book we treat a closely related topic: Loewner's theory of monotone matrix functions and his analytic continuation theorem which guarantees that a real function on an interval of the real axis which is a monotone matrix function of arbitrarily high order is the restriction to that interval of a Pick function. In recent years this theorem has been complemented by the Loewner-FitzGerald theorem, giving necessary and sufficient conditions that the continuation provided by Loewner's theorem be univalent. In order that our presentation should be as complete and trans­ parent as possible, we have adjoined short chapters containing the in­ formation about reproducing kernels, almost positive matrices and certain classes of conformal mappings needed for our proofs.

Edition details

• Publisher: Springer
• Publication date: 2011
• Language: English
• ISBN 10: 3642657575
• ISBN 13: 9783642657573
• Binding: Paperback
• Number of pages: 194