Numerical Range of Holomorphic Mappings and Applications
This book describes recent developments as well as some classical results regarding holomorphic mappings. The book starts with a brief survey of the theory of semigroups of linear operators including the Hille-Yosida and the Lumer-Phillips theorems. The n
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Numerical Range of Holomorphic Mappings and Applications
Mark Elin • Simeon Reich • David Shoikhet
Numerical Range of Holomorphic Mappings and Applications
Mark Elin Department of Mathematics ORT Braude College Karmiel, Israel
Simeon Reich Department of Mathematics The Technion - Israel Institute of Technology Haifa, Israel
David Shoikhet Department of Mathematics Holon Institute of Technology Holon, Israel Department of Mathematics ORT Braude College Karmiel, Israel
ISBN 978-3-030-05019-1 ISBN 978-3-030-05020-7 (eBook) https://doi.org/10.1007/978-3-030-05020-7 Library of Congress Control Number: 2019934203 Mathematics Subject Classification (2010): 46G20, 46T25, 47H20, 47D03 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
This book is dedicated with deep appreciation to the memory of our friend and colleague Professor Jaroslav Zem´anek (1946–2017)
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
1 Semigroups of Linear Operators 1.1 Linear operators. Spectrum and resolvent . . 1.2 Continuous semigroups and their generators . 1.3 Numerical range of linear operators . . . . . 1.4 Analytic semigroups . . . . . . . . . . . . . . 1.5 Ces` aro and Abel averages of linear operators 1.6 Abel averages: recent results . . . . . . . . .
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2 Numerical Range 2.1 Holomorphic mappings in Banach spaces . . . . . . 2.2 Spectrum and resolvent of holomorphic mappings . 2.3 Numerical range . . . . . . .
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