Foundations
The first section of this chapter introduces the complex plane, fixes notation, and discusses some useful concepts from real analysis. Some readers may initially choose to skim this section. The second section contains the definition and elementary proper
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Graduate Texts in Mathematics Series Editors: Sheldon Axler San Francisco State University, San Francisco, CA, USA Kenneth Ribet University of California, Berkeley, CA, USA
Advisory Board: Colin Adams, Williams College, Williamstown, MA, USA Alejandro Adem, University of British Columbia, Vancouver, BC, Canada Ruth Charney, Brandeis University, Waltham, MA, USA Irene M. Gamba, The University of Texas at Austin, Austin, TX, USA Roger E. Howe, Yale University, New Haven, CT, USA David Jerison, Massachusetts Institute of Technology, Cambridge, MA, USA Jeffrey C. Lagarias, University of Michigan, Ann Arbor, MI, USA Jill Pipher, Brown University, Providence, RI, USA Fadil Santosa, University of Minnesota, Minneapolis, MN, USA Amie Wilkinson, University of Chicago, Chicago, IL, USA
Graduate Texts in Mathematics bridge the gap between passive study and creative understanding, offering graduate-level introductions to advanced topics in mathematics. The volumes are carefully written as teaching aids and highlight characteristic features of the theory. Although these books are frequently used as textbooks in graduate courses, they are also suitable for individual study.
For further volumes: http://www.springer.com/series/136
Rub´ı E. Rodr´ıguez • Irwin Kra • Jane P. Gilman
Complex Analysis In the Spirit of Lipman Bers Second Edition
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Rub´ı E. Rodr´ıguez Facultad de Matem´aticas Pontificia Universidad Cat´olica de Chile Santiago, Chile
Irwin Kra Department of Mathematics State University of New York at Stony Brook Stony Brook, NY, USA
Jane P. Gilman Department of Mathematics and Computer Science Rutgers University Newark, NJ, USA
ISSN 0072-5285 ISBN 978-1-4419-7322-1 ISBN 978-1-4419-7323-8 (eBook) DOI 10.1007/978-1-4419-7323-8 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012950351 © Springer Science+Business Media New York 2007, 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered na
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