Monotone Matrix Functions and Analytic Continuation
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
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Herausgegeben von
S. S. Chern J. L. Doob J. Douglas, jr. A. Grothendieck E. Heinz F. Hirzebruch E. Hopf W. Maak S. MacLane W. Magnus M. M. Postnikov F. K. Schmidt D. S. Scott K. Stein Geschdftsfilhrende H erausgeber B. Eckmann 1. K. Moser B.L.van derWaerden
William F. Donoghue, Jr.
Monotone Matrix Functions and Analytic Continuation
Springer-Verlag Berlin Heidelberg New York 1974
William F. Donoghue, Jr. University of California,Irvine, California 92664, U.S.A.
Geschaftsftihrende Herausgeber B. Eckmann Eidgenossische Technische Hochschule ZUrich J. K. Moser Courant Institute of Mathematical Sciences, New York
B. L. van der Waerden Mathematisches Institut der Universitat ZUrich
AMS Subject Classifications (1970): Primary 26 A 48, 30 A 14, 47 A 10 Secondary 15 A 18, 30 A 31, 30 A 32, 30 A 80
ISBN -13:978-3-642-65757-3 e-ISBN -13 :978-3-642-65755-9 DOl: 10.1007/978-3-642-65755-9
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by ilhotocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Bedin Heidelberg 1974. Library of Congress Catalog Card Number 73-15291 Softcover reprint of the hardcover 1st edition 1974
William F. Donoghue, Jr.
Monotone Matrix Functions and Analytic Continuation
Springer -Verlag New Yark Heidelberg Berlin 1974
William F. Donoghue, Jr. University of California, Irvine, California 92664, U.S.A.
Geschaftsfiihrende Herausgeber B. Eckmann Eidgenossische Technische Hochschule ZUrich J. K. Moser Courant Institute of Mathematical Sciences, New Yark
B. L. van der Waerden Mathematisches Institut der Universitlit ZUrich
AMS Subject Classifications (1970): Primary 26 A 48, 30 A 14, 47 A 10 Secondary 15 A 18, 30 A 31, 30 A 32, 30 A 80
ISBN -13: 978-3-642-65757-3 e- ISBN -13: 978-3-642-65755-9 DOl: 10.1007/978-3-642-65755-9
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re~use of illustrations, broadcasting, reproduction by ilhotocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer·Ver· lag Berlin Heidelberg 1974. Library of Congress Catalog Card Number 73·15293. Monophoto typesetting and offset printing: Zechnersche Buchdruckerei, Speyer. Bookbinding: Konrad Triltsch, Wlirzburg.
Foreword
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 func
